Chicken Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠃⠏⢇⢠⠖⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢸⠇⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢀⡞⠀⢸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠈⠀⠀⠈⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠨⠀⡄⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢖⠀⠂⠀⢀⠀⢰⠀⢠⠀⠀⣼⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣒⠶⠤⢤⣀⣀⣤⠤⠴⠖⠂⠐⠋⠱⣩⣿⣦⠀⠰⠸⡄⠀⠃⠀⠋⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠁⠀⠀⠀⠀⡤⠞⠀⢇⠿⢿⡁⠀⠘⠁⠙⢆⠀⠀⢰⣾⡧⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢴⠖⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢤⣀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠈⠩⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠔⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠾⠃⠀⠘⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠐⠀⠀⠀⢀⢈⡓⢦⡀⠀⠀⣧⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠁⠀⣀⠀⠀⠀⣣⠀⠀⠐⠶⠖⠀⣂⠀⢘⠳⠲⣄⠙⢄⡀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀⠀⢠⠎⠀⡼⠋⠀⠁⠀⠀⣞⡀⠀⠉⠛⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠰⡇⠀⠀⠀⠀⠼⠀⠀⠀⠈⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡃⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠹⡆⡞⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠊⠀⠀⠀⠀⠀⢐⡅⣠⣠⠆⠀⠀⠈⢇⠀⠀⠀⠀⠀⣀⠴⠻⠈⠃⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠀⠀⠀⠀⠀⠀⡄⠈⠁⠀⠀⠈⠀⡄⠈⠑⠦⠶⠖⠋⡅⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠈⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠠⠀⠂⠀⣠⢀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠴⠂⠀⠀⠀⢀⡄⠀⠐⠣⠋⢀⣾⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠄⠀⠀⠀⠈⠁⠀⡴⠀⢀⠎⠀⠀⣠⠟⠀⠀⠀⠀⠀⠸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠔⠂⠸⠤⠀⠈⠰⠖⠋⠁⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢊⠀⠀⠀⣠⠎

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠢⡀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠘⠁⠀⢱
⠀⠀⠀⠀⡐⠉⠈⠑⠃⠀⠀⠐⠀⠐⠀⠘⠂⠢
⠀⠀⠀⠀⢃⠀⠀⠄⠀⡀⠀⠀⠁⠀⠐⠀⠀⠸
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠈⠣⣀⠠⠀⠀⠀⢀⠀⡐⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⠖⠉⠀⠀⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⡀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠢⡀⠆⠈⠀⢠⠀⡠⠊⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢀⢀⠠⡙⠁⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠇⠀⠘⢨⠖⠁⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⢆⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠈⠢⠀⠀⡄⠂⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢈⠈⠈⢀⠕⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⢀⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠌⠁⢺⠁
⠀⠀⠀⠀⠀⠀⡀⠔⠃⠀⢀⣀⠀⠀⠀⢀⣀⠀⢀⠇⠈⡡⢊⠒⠤⢀⡀⠀⠀⠀⢀⡀⣤⠒⠈⠀⢀⡀⢸
⠀⠀⠀⢀⡴⠊⠀⠀⠑⠊⠁⠀⠑⠤⠤⠃⠈⠁⠁⢀⠜⠀⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠆⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠸
⠀⠀⠀⢇⠀⠀⠀⠀⢰⠀⠀⠀⠢⠂⠀⠀⠐⠀⠐⡀⠈⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠹⠂⠀⠀⠈⡄⠐⠀⠀⠀⠐⠀⠀⠀⠀⠉⠒⠂⠉⡇⠀⠀⠀⠀⠈⠠⠀⠀⠂⠆⠀⠀⠀⠰
⠀⠀⠀⢠⠁⠀⠀⠀⠀⠰⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠐⠂⣡⠙⠢⠀⠠⠊⠀⠀⠐⠀⡆
⠀⠀⠀⠀⠂⠄⠠⠄⠀⠀⢣⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠱⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠤⣀⣀⠀⠀⠀⠀⠀⢀⣀⠠⠠⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠉⠀⠈⠀⢹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⡀⠀⠀⠀⠘⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢔⠅⣕⣀⣠⣔⠧⢨⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠂⠀⠀⠀⠘⠃⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡠⢶⠿⠿⠆⠶⠶⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡖⠂⠰⠛⠈⠛⢛⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⢤⣀⣠⣄⣠⣄⢀⣀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡧⠀⢀⣠⣴⣾⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠿⠛⠛⠛⠋⠈⠉⠙⠛⠋⠙⠉⠛⠻⠆⣤⡄⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠛⣫⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠉⠠⣦⠀⠀⠀⢀⣴⡄⠀⠀⠀⠘⠿⠂⠀⠀⠀⠀⢀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡍⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋
⢠⣤⣶⣤⣀⣴⡶⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⣀⠀⠀⠀⠀⠀⠀⣯
⣈⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠶⠿⢷⣤⣤⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⢀⣿⡆
⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⢸⣿⣭⣶⠶⠮⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠁⠀⠀⠀⢀⣼⡟
⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⣛⣛⠛⠷⢤⣴⣶⠆⠀⠀⠀⣀⣤⡄⠺⠛⠉⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⣉⣉⣭⣤⣶⣶⣶⣧⣤⣴⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟
⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠉⠛⠛⠉⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⢀⢠⣤⣿⠟⠃
⠀⠀⠀⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⣯⠤⠆⠀⠀⠀⠀⣰⣿⠉⠉
⠀⠀⢸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣤⣦⣤⡾⡿⠇
⠀⠀⠀⠉⣿⣷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⠛⠉⠉⠀⠉
⠀⠀⠀⠀⠘⠋⠉⢉⣴⣶⣤⣄⣀⠀⠀⠀⠐⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠙⠛⠂⠰⢄⣴⠟⠉⠀⠀⠀⠀⢀⣀⢀⣀⢠⣴⣶⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⣀⣀⣴⠟⠻⢮⡉⠛⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡄⠀⢼⣿⠋⠁⠀⠀⠀⠙⢦⡈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠘⣧⠀⠀⠀⠀⠀⠀⠀⠹⣦⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠘⣷⡀⠀⠀⠀⠀⠀⠀⠈⢷⡌⠻⣦⣄⣀⣀⣠⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡘⣷⡀⠀⠀⢀⣤⣤⡴⢾⣃⣄⡀⠨⣙⣻⣿⣶⣾⠿⠟⠻⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡈⠻⣄⡀⠘⠛⠛⠚⠉⠉⠉⠉⠓⠶⣯⣭⣛⠾⢯⡛⠋⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠇⠀⠈⠻⣿⣓⣀⣛⣛⣿⣽⠿⠷⠀⠀⠀⠉⠛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣚⠉⣥⡶⢦⡄⢶⣤⣤⣤⣉⣉⣉⣉⣋⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉⠀⠀⠀⠈⠻⣆⡙⢦⡀⠀⠀⠉⠉⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢾⣿

⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠲⣤⡀
⠀⠀⠀⡼⡩⠖⠛⠓⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⡇⠀⢻⠈⢇⡟⢲⡀
⠀⠀⢀⣟⡄⠙⢨⡇⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⡁⠀⠀⠀⡼⠀⠜⠩⢧
⠀⠀⠈⠸⡀⢳⠌⠁⠀⠀⠀⢠⣀⡙⢆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠀⠀⠀⠢⡁⠀⣀⡴⠊⣧⡀
⠀⠀⠀⠀⠉⣻⠀⠀⠀⠀⠀⠀⡉⠛⠗⠱⣄⠀⢀⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠉⢀⡤⣸⠁
⠀⠀⠀⠀⠀⡇⠀⠜⡸⠆⠓⠀⠀⡀⠀⠀⠋⢉⠉⠁⠫⠤⣀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⣨⠂
⠀⠀⠀⠀⢰⡇⠀⠶⠇⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠠⢄⠊⠀⠀⡰⠀⠀⠀⠙
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣇⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢄⠀⠀⠀⢀⠞⠀⢀⠂⠠⠤⢀⡠⢞⠀⠀⠘⣤⠋
⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢤⡀⠋⠂⢀⡡⠔⠋⠉⠁⠀⠈⠙⣶⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠚⠁⠀⠀⠀⠀⠀⠀⠂⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣦⡀⠀⠀⢠⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠆⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣀⣀⣀⠀⢠⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⢀⣠⣽⣭⠽⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣀⣀⣠⠞⠷⢴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡰⠃⠀⠀⠀⢿⡄⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁⠀⠀⣀⣀⣨⣟⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣻⠾⠉⠓⠒⠚⠂⠈⠿⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣠⣴⣾⣯⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⢿⠵⠀⠀⡿⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⣤⡁⠶⣿⠖⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⠀⣰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⢿⣙⣾⣿⣾⣿⣽⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣡⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠇⠀⠉⠁⠀⢬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡟⣟⡛⢻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠇⠀⠀⠀⠀⢠⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⢾⣿⣿⡟⠳⣾⣀⣽⠿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠃⡀⠀⠀⠀⣹⣿⣿⣿⣿⢿⣿⢛⣳⠶⣶⣾⠿⣿⣿⣿⣿⣷⠿⢥⣀⣹⣇⣀⣒⣉⣽⠟⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣜⠀⠀⢀⣶⣿⣿⣿⠛⠲⣾⣭⡭⢿⠖⠿⠿⣯⣨⣿⠿⠿⣿⣷⣤⣌⣩⣿⠍⠉⣱⣿⡛⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠀⢠⣼⣿⣿⡟⠛⠿⣿⡿⠶⢾⡛⢛⣿⠟⣁⣈⠉⠀⢀⣈⠛⠙⢿⣶⣍⠛⢻⣿⠃⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣦⢠⣿⣿⡿⠏⠙⠻⣿⠻⠶⣤⣶⢛⣿⠓⡾⢉⣥⣴⣶⠶⢶⡶⣷⣾⣿⣿⣿⠋⢛⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⢸⣿⣟⣱⣄⣉⣹⣟⣳⣾⣋⣿⣫⣔⣾⣿⣿⣿⠻⢷⣄⡰⠂⠠⣿⠛⠛⠻⣿⣿⣿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣇⣿⢟⠿⠿⠻⣿⣿⣿⣉⣻⣴⣚⣷⣿⣷⡉⠈⠳⣤⣀⣰⣷⠖⠲⢋⣀⣉⠀⠙⠃⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⡈⠀⠀⠀⠀⠈⠉⠛⠋⣹⡿⢿⣿⣧⠉⠁⠀⠈⠁⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠸⠓⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⢂⡀⢀⠀⢀⡀⢀⣀⣀⣄⣀⠀⡀⠀⠀⠀⠄⢤⠠⢀⠀⣺⣧⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣤⣊⡐⢴⣛⡟⠽⠛⠬⣿⢿⣿⣷⡆⠀⠀⢺⣄⠈⠁⠙⢧⣙⣿⣿⣍⡧⠠⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⣿⣿⣿⣿⣷⣾⣤⣬⣿⣿⣧⡀⠀⠸⣿⡌⣷⣀⠀⠉⢻⣿⣿⣾⠀⣡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣧⡀⢠⡹⣿⣿⣏⠁⠀⠙⣿⡿⠿⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠉⠛⠻⢯⣿⣷⡬⠛⠷⢤⠣⡶⣮⠹⢿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢿⠿⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⣤⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⡴⠁⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⡿⠿⢷⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠰⠶⣈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣄⣾⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⢀⣮⣱⣤⣵
⠀⠀⠀⠀⠀⠀⠀⢰⡶⣼⣿⡈⢻⣇⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⢾⣿⢿⡿
⠀⠀⠀⠀⠀⠀⣀⣘⣿⣌⠻⣿⡄⢻⣎⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⡀⠀⠀⠀⣿⡍
⠀⠀⠀⠀⠀⠈⣿⣌⠙⢿⣧⡘⢿⣮⣻⣮⣆⡀⠀⠀⠀⡀⠀⠄⠀⢀⠀⠀⠀⠀⢡⣤⣭⣿⡇
⠀⠀⠀⠀⠀⣀⣈⣿⣷⣄⠙⢿⣦⣽⡟⠛⠆⢀⠀⠀⢠⠀⠀⠒⠀⣐⣦⠖⢻⣷⣧⣏⡟⣿⡇
⠀⠀⠀⠀⠀⢻⣮⣉⠛⠻⣿⣦⣹⣇⠉⢲⡂⠈⠒⠀⢰⣀⣀⣹⣋⣩⠿⢶⣇⡜⢹⢿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠙⣿⣷⣦⣄⡙⠻⣍⠙⢶⡛⠳⠶⠦⢽⣋⢁⣚⣿⣥⡴⠋⡻⢿⣷⣾⣾⡟
⠀⠀⠀⠀⠀⠀⠀⢿⣭⣛⠻⢿⣿⣾⣷⣾⣟⠲⠶⠬⠭⠿⣏⣀⡬⢿⢷⣾⣤⣎⡸⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣶⣬⣭⣽⡿⣷⢶⣤⢭⣭⠿⣿⣤⡴⢋⡹⢿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣻⡷⢶⡷⣶⠛⢿⣅⣴⠛⣿⣷⣾⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⠶⡿⢶⣟⣩⡿⢺⣷⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣻⣯⢼⣿⣻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡙⠉⠉⠙⠛⢿⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠠⠤⣄⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠥⠤⠄⠁⠿⠇⢀⡿⠁⠀⠐⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠮⠥⠤⠤⠤⠬⠭⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣮⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⠥⣴⠛⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⢠⣟⣰⣿⣿⡟⣷⢾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠛⣉⣵⢿⣿⡍⠁
⠀⠀⠀⠀⠀⠀⠠⠴⠶⣿⣿⣿⣿⡧⣀⠝⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⣯⠉⣭⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣷⣮⣄⡢⠉⠵⠖⠲⠶⣤⣦⣴⡾⠃⠒⢲⣠⢠⣄⡋⢁⣤⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣧⠕⡉⠀⣥⠗⠲⠀⠬⠟⣹⡄⠀⠀⠠⣈⣩⡶⠟⠂⠙⠛⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣻⢱⣨⡶⣇⡗⡟⢤⠀⣙⣷⣄⠐⣣⡶⢤⡽⠁⣾⠃⠀⠀⠀⢀⣾⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣾⣹⢾⣛⡧⢏⣹⣉⡄⢸⣿⣿⣿⡧⠍⠛⠁⣈⡍⢈⣒⣒⣾⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⢿⣻⣬⣏⣛⡴⡷⠼⣉⣡⠬⠟⢿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⣧⣽⡡⢬⣏⣹⡶⢯⢽⡂⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣿⣿⣷⣇⣽⡝⣤⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢜⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣴⣄⣀⡀⡀⠀⢀⡀⢀⠄⡼⣮⢆⣡⣖⣀⡀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⡠⣠⡤⣠⣄⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡾⢣⣿⣿⣿⡿⣿⣿⣶⣶⣿⣿⣷⣣⢞⣵⣠⣀⣤⣤⡄
⠀⠀⠀⠀⠰⠁⠗⠓⠛⠟⠾⠟⠛⢛⣿⠟⣽⡿⣿⢿⣿⣟⣿⡿⣢⣿⣿⡿⠋⠼⡿⣫⠽⠯⠿⠋⠙⠉⠙⠛⠛⠙⠋⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠈⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠴⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⢠⡗⢐⡖⣛⣑⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠼⣌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠛⢿⣏⡹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠄⠶⠀⠆⠈⢆⠈⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢆⠀⠐⡌⠀⢦⠀⠀⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡘⣦⢑⠸⠄⠼⠆⠶⠻⣧⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠑⢦⡉⡀⣀⡀⣠⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠖⠈⠻⢦⡎⠭⢥⡜⢻⡁⠴⠆⢀⡀⠀⠀⠀⠀⠀⠀⣀⠖⣿⢳⢌⣡⣁⣠⠛⠡⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⠆⢸⡆⣉⣭⠒⣓⣚⢭⠆⢿⡀⣀⠳⣦⠔⣦⠌⠻⢴⡛⡄⣵⡆⣁⢇⡘⢛⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣥⠟⢋⣄⣹⠋⣩⣖⣩⣝⠉⢴⢸⠇⢠⠻⣆⠉⣻⡗⡸⠧⠻⢘⡉⠑⠊⢛⠁⣌⣙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠙⠺⢧⡉⡍⠀⣉⣉⡡⠺⣶⣉⣿⠒⣻⣿⠏⣤⡼⢙⣷⠻⣯⣈⣘⠙⠿⠚⠛⠒⣡⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣯⢈⣵⠛⠻⠋⣅⡲⠶⠶⠶⣤⣆⣩⡷⣊⣽⣻⡉⠼⢤⣨⡟⣹⢘⠴⣧⢻⣛⣇⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣟⢣⡴⢷⡊⣷⢚⡜⣤⣌⢝⡉⠹⠧⠾⣗⣉⢤⡄⡋⣭⠁⠾⣔⣠⢣⣀⣩⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣞⣿⣴⣦⣍⣹⣓⣿⣾⣿⣛⣿⡟⢛⣥⣼⢑⡏⢸⣧⢘⠙⣣⣨⣱⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢟⠿⣿⣩⡭⠛⡙⠿⣿⠲⣭⣦⣭⣥⣬⣥⣉⣾⣾⣷⣇⣼⣿⣭⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣟⣽⣶⣗⣻⠴⢞⣿⠂⣚⣭⣽⣒⣒⣛⣩⠿⣻⣿⣿⣷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣽⣷⣯⣵⣟⣴⢟⣽⣿⣿⣿⣭⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢿⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣞⣾⣟⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠙⣿⣿⣿⣗⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠁⠈


⣿⢿⠿⠿⠿⢟⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣻⣻⣿⣿⣿⣟⣿⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⣶⣼⣆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⠿⠿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠁⠲⢓⢠⡉⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄⢠⠃⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣷⣄⡬⣴⠁⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣠⢃⡜⠰⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠟⠛⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⠇⡘⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡀⢈⣀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⣠⠄⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⠢⢄⣤⣤⠖⠚⠙⠋⠉⠉⠀⠀⠀⠠⡘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠢⠀⣄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⠤⡀⠀⠀⢄⠀⠈⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⠀⠀⠐⠂⠀⠀⠀⠀⠀⠠⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⢀⢀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠈⢠⠠⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡰⢄⡠⠁⠠⠜⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⢢⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡑⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠉⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⢑⣲⡾⠦⣄⠀⠀⠀⠀⢠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣏⡽⠀⠀⠀⠀⠉⠒⠢⢴⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡏⠀⠀⠀⠀⠀⡀⠀⠠⣤⠀⢻⠙⢄⡀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⡶⢯⡥⢼⡞⠡⠀⠀⠉⠐⠀⠠⠔⠒⢿⠇⡘⡛⠤⠕⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣠⠌⣉⠁⠈⡂⠀⠀⠀⠀⠂⣀⣀⣀⠢⢉⠒⠈⠁⠌⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢲⠟⠉⠐⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠠⡾⢂⣏⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠓⠿⠷⠮⢤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠐⠐⢆⠒⠀⠀⠐⢉⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠐⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⠖⠋⣏⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢀⠎⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡄⢠⡏⠀⠀⠀⠀⠀⠐⡞⠂⠄⢀⠀⠀⠠⡀⢀⠀⠀⠀⡀⠀⠀⠀⠊⡠⠈⢁⡤⠢
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠈⠁⠀⠀⢀⣀⣀⡗⠊⠁⠀⠀⠀⠉⠋⠚⠃⠒⠂⠀⠈⢀⡀⠀⠀⠉⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠑⠂⠑⠤⠔⠙⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⢀⢀⠤⠰⠀⢀⠠⠂⠁⡘⠀⠐⠋⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠁⠀⠀⠀⠉⡤⠔⠊⠁⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠈⠄⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⠤⠒⡀
⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠨⠤⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠑⠢⣀⡈⠀⠀⠀⠄⠀⣀⢀⣠⠔⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⡀⠠⠀⠀⠉⠙⠒⢒⠒⢒⠒⠒⠀⠂⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡐⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⡀⢠⣄⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⡤⡤⠤⠤⡴⠄⠀⠀⠀⢀⡠⠋
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡮⢽⢻⣍⣅⡈⢰⢲⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⠒⣛⡟⡒⢹⠿⢿⡏⠙⣈⣶⣰⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠭⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣷⣼⣧⣿⣧⣾⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⢤⣤⣀⠀⣅⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⡀⠀⣀⠀⠙⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠼⠋⠀⢀⣀⣀⠉⠽⢿⣮⢶⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⢨⠛⠀⠉⣠⣶⡤⠘⠂
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠿⢻⣿⣷⣦⡙⣷⢳⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠈⠳⠤⣼⣿⠏⣧
⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⠤⠴⠟⠒⠲⣿⣿⣮⢿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠕⡁⠀⠀⠀⠀⠀⠀⠸⢟⣠⠃
⠀⠀⠀⠀⠀⠀⣿⣡⡎⢁⣠⡶⠆⠀⠀⠀⠉⠛⠃⢹⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠙⡀
⠀⠀⠀⠀⠀⢠⣯⣤⡴⠛⢱⣛⣯⣽⢿⣽⡦⡀⡄⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡿⢫⠇⢀⢀⢀⠁⠀⠀⠀⠀⠠⡀⠀⢃
⠀⠀⠀⠀⢀⣿⣿⠿⣡⣦⣿⣿⣛⣟⣿⣷⣝⣦⣰⣦⢼⣄⣀⣀⣀⣀⣠⠤⠀⠘⠀⡁⠀⣳⠀⡈⣼⠘⢀⠀⢢⠀⠀⠁⠄⢸⡀
⠀⠀⠀⠀⢸⣿⡟⢠⣿⣿⣿⡵⠛⠋⠉⢀⣠⢯⣴⠾⠿⠶⠾⣿⣿⣁⣟⡗⠾⠀⡠⢫⡇⠿⠈⡁⠈⡄⠘⣇⠠⠣⠡⠀⠌⠠⡇
⠀⠀⠀⠀⢸⣿⡇⣾⣿⡿⠑⢋⣴⣿⢗⠔⣾⡿⢁⣠⣤⠀⠐⣾⠏⢁⠈⠷⠲⠚⠴⢿⡶⠃⡰⡇⣼⢃⠀⠸⡇⠇⠄⠀⡀⢰⠃
⠀⠀⠀⠀⠈⢿⣧⢿⣿⡇⢀⣿⢱⡏⡾⠃⣻⢃⡾⠋⠀⣠⣿⠏⢌⣲⣆⠐⠌⣻⡄⡰⣄⣠⠄⢐⣩⣬⢠⠆⡦⠰⠠⠁⢂⡞
⠀⠀⠀⠀⠀⠈⠻⡌⢿⠃⢸⣧⣿⣷⣧⣞⣿⡟⣠⠀⣾⢫⡳⣌⡀⢒⠆⡛⢛⣭⡬⠡⠶⢖⡶⣪⣝⣧⠏⣴⠃⠍⠄⢄⠞
⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⢸⣿⣿⣿⡿⣸⣿⡴⢁⡼⠁⣨⣽⠀⠥⡈⠳⠶⠖⣲⣭⠜⢣⣬⣥⡿⣉⣥⡾⢋⣁⠸⡷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡏⣿⣿⣿⡇⣿⣿⣣⣾⣷⣿⡿⠿⢓⣶⣦⣝⣻⣴⣶⣶⣿⣶⣶⡶⣿⣿⣿⡿⡞⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠣⣿⣿⣿⡇⣿⣿⣿⣿⡿⠃⠀⢀⠀⢒⢀⡉⠉⡰⡝⣻⢿⣟⣿⣿⣿⣿⣿⣆⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠻⡝⢩⣿⣿⣿⣿⣧⣶⣦⢈⡀⠲⢤⢠⣴⣇⣿⣟⣿⣿⣿⢿⣻⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡛⠁⠘⣿⡹⠃⠙⢷⣶⣰⢴⣦⣤⣶⣾⣿⣿⡟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠛⢥⡭⠟⠝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢂⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢧⣀⠿⣶⡤⠴⣴⣦⡤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡮⠼⢮⣓⠦⠬⣥⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠛⠑

⣀⣠⡅⠀⠀⠂⢀⡀
⡟⠛⢡⣼⡄⣼⡏
⢦⡜⠓⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⢸⣿⡆
⠘⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣄⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⣻⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠻⣿⣧⡀⠀⠀⢠⣿⡄⠀⠀⠀⢸⣿⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣀⠿⠷⠀⠀⠈⠿⠃⠀⠀⠀⣨⣿⠀⠀⠀⢀⣿⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠀⠀⢠⣾⣿⠀⢰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠋⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠄⡀⠀⠀⠀⠠⠄⠋⠉⠀⠀⠐⠲⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠸⠗⠀⠀⠘⠀⠀⠀⠀⠄⠈⠂⠂⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡦⠂⣀⣀⡿⣶⣦⠹⣶⢀⠀⠀⠀⠀⠀⢄⡀⠀⢀⠀⠆⠈⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⠠⠄⠀⠈⢿⣀⡘⡤⡦⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡄⠆⢠⡄⠀⠉⠻⠇⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠛⠉⣟⣻⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣧⣶⠀⠀⠀⠀⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣦⣄⠀⢸⣿⣿⣿⠸⣿⢻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⡀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡟⣿⣾⣿⣿⣿⡿⠀⠙⠻⢿⣿⣷⣾⣿⣻⣿⣿⣿⣿⣬⣉⣼⣿⣿⣿⠟⢀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⣠⣶⣿⣟⣿⣿⣿⢻⣷⠸⣿⣿⣿⡟⠀⠀⠀⢀⣀⣠⣿⣿⣿⡿⡿⢿⣿⣿⣽⣿⡟⣩⣵⣿⠀⢸⣯⡿
⠀⠀⠀⢀⣤⣾⣿⣿⠿⢋⣿⣿⡏⣸⣿⡆⠘⣿⣿⣿⣾⣿⣿⣿⣿⣿⣍⠛⣋⣭⣵⣶⣿⣧⣤⣿⢿⣯⣿⣭⣧⣾⡟⠁
⠀⢀⣴⣿⣿⣿⠟⢀⠴⣻⣿⣿⣇⠹⢿⠟⠀⣿⣿⣿⣿⣿⣧⡿⠿⠿⢿⣿⣷⣿⣼⣏⠉⠛⠯⣍⠀⠈⠉⠈⣿⣿
⣴⣿⣿⣿⡿⠏⢀⠓⢈⣿⣿⣿⣿⣿⣶⣄⠀⣼⣿⣿⣿⡿⣉⣤⣾⣿⣷⣿⠿⣡⣦⣿⠂⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆
⣿⣿⣻⠟⠁⠄⠃⣰⡟⣱⢟⣿⢿⣿⣿⣿⡄⣿⣿⠟⣉⣴⠋⣼⣿⣿⣿⣿⣄⣼⣿⠛⣿⣷⣶⣄⡀⠀⠀⠀⠀⢿⡇
⣿⢷⡟⠁⠀⢠⡾⢫⠘⣁⠋⠀⢈⣿⣿⣿⣿⡟⢡⣿⣿⢁⠈⣿⣿⣿⡾⠁⠛⢿⣿⣆⢹⣿⣿⣿⣿⠑⠒⠦⢄⣘⡇
⠻⠆⠀⢀⡼⢋⡔⠃⠀⢀⡞⠀⢸⡇⢸⣿⡿⢡⣿⣿⣯⣾⢠⣿⣿⣿⣷⣈⣧⡾⣿⡿⠂⣿⣿⣿⣿⣿⣦⡄
⠁⢀⠀⠉⢠⠊⠠⠀⣠⣿⠂⠀⠏⡇⣸⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⡇⣼⠟⢻⡗⠛⣿⣿⣇
⠀⠀⠀⠀⠁⠠⠀⣴⠛⠏⠀⢠⢰⡇⣿⣿⠀⠹⣿⣿⣿⣟⡿⠉⠈⣿⣿⣿⣿⣹⡿⣱⣿⣿⡟⠁⠀⠙⠿⠸⡀
⠀⠀⠀⠀⠀⠀⠸⠃⢺⠀⠀⠀⢈⢀⣿⣿⣷⣀⠛⠿⣿⡟⠁⠀⠀⠀⣿⣿⣿⢹⣷⣿⣿⡿⣟⡀⠀⠀⠘⢶⡇
⢠⡎⠀⠈⠀⠂⠀⠀⠘⠀⠀⠀⠀⡼⢯⢹⣿⣿⣷⣤⡘⡌⠀⠀⠀⣸⣿⣿⣿⣿⣽⣿⣿⣷⣿⣧⠀⠀⠀⡼
⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⣿⢱⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠸⣿⣿⣿⠧⢼⣿⣿⣿⣿⣿⠀⠀⢐⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣤⣸⣿⡿⣎⣃⣼⢿⣿⣿⠟⢡⠂⣠⠎
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢰⣇⣀⣿⣿⣿⡿⣿⣇⢡⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣫⣟⣚⠿⠄⣃⣠⡟⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡟⢹⣿⣯⣿⣿⣿⣧⣾⢻⣿⣏⣿⣿⣿⣿⣿⣿⣿⠋⠈⠀⡡⢴⣵⠟
⠀⡀⠀⠀⠀⢠⣿⠀⣿⣻⣷⣿⣧⢿⣿⣿⣿⡿⣠⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣩⣴⠟⠁
⠀⠁⡄⢰⢀⡿⣿⠀⣷⣾⣧⣿⣿⣾⣿⣿⣿⣟⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿
⢀⡄⣵⣾⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⡗⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣇⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⠀⣿⢿⣿⣿⣿⣟⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡄
⠈⠠⣿⣼⣯⣾⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣸⣿⠇⣻⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠢⣄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠊⠁⠈⡆
⠀⠀⠀⠀⢠⠒⠀⠒⠾⠀⠀⠈⠂⠀⢄⠀⠓⠂⢄
⠀⠀⠀⠀⢠⠀⠀⠠⠀⣀⠀⠀⠘⠃⠀⠤⠒⡄⡸
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠈⠢⡀⠢⡀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣐⣀⠔⠂⠀⠘⠺⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⠀⠤⠀⢁⠀⢀⠴⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⣀⠀⠀⠀⠀⠶⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠘⢾⠀⠀⡆⢸⡰⠋⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠛⠱⡎⠉⢙⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠂⢄⡘⠀⢠⢘⠔⠁⡀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠜⠤⠜⠑⡄⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠁⠀⠘⠃⠀⠐⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠦⠤⠤⠒⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠜⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⡇
⠀⠀⠀⠀⠀⢀⠴⠊⢉⣀⡠⠤⢄⠀⠀⢀⡔⢤⡀⠜⠀⢀⠔⡁⠉⠑⠢⠤⠄⠀⠠⠄⠴⠒⡋⠀⠀⠀⠠⠀⡆
⠀⠀⠀⢀⠞⠁⠀⠀⠈⠁⠀⠀⠀⠑⠒⠊⠀⠀⠀⠀⡰⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠢⠂⠀⠀⡇
⠀⠀⠀⡎⠀⠀⠀⠀⠘⠀⠐⠐⠀⠀⠐⠂⠀⠀⠀⠰⠁⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠈⠀⠇
⠀⠀⠀⠱⣀⠀⠀⠀⠀⡇⠀⠀⠈⠊⠀⠀⠀⠉⠀⠠⡀⠀⠉⣠⡄⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸
⠀⠀⠀⠀⢠⠃⠀⠀⠀⢰⠈⠁⠀⠀⠀⠉⠀⠈⠂⠀⠈⠉⠉⠀⡇⢁⠀⠀⡠⢂⠑⠀⠤⠂⡘⠀⠀⠀⠀⡎
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⡆⠀⠀⠈⠀⠀⠂⠀⠀⢀⠀⡀⠀⠀⢣⡀⠁⠀⣠⠊⠑⠦⠀⠊⠀⠀⠐⠁⢰⠁
⠀⠀⠀⠀⠑⠤⠤⢤⠀⠀⠘⣄⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠈⣦⡀⠀⠀⠀⡠⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣀⠀⠀⠀⢀⡴⠁
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠋⠁⠙⠦⣀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠠⠠⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⣄⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠔⠊⠁
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡏⠉⠉⠉⢹⠀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠇⠀⠀⠀⢸⢠⠁
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⣁⣳⣄⣀⣤⣾⢘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠸⠁⠉⠉⠁⠸⠎⠙⠁
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⣶⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⢸⡏⣹⠅⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠙⠋⠓⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠃⠄
⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠈⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⡤⠴⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⢀⠌⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡅⢀⡇⠀⠀⠀⠀⠠⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠔⢁⡠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠑⠊⠀⠀⢀⠀⣰⠔⠊⠀⠀⠈⠒⠚⠺⠶⠵⠀⠀⢀⠀⠀⠀⠂⢁⠄⠋
⠀⠀⠀⠀⠀⠀⠓⠛⠄⠒⠄⠄⠓⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⡀⠔⠉⠸⠀⠐⠊⢁⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁⠀⠀⠀⠉⡤⠔⠊⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠡⡀⠀⠀⠐⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⢬⡄⠔⠂⠄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⢄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⠤⢀⡀⠀⠂⠀⣄⠐⠒⠛⢩⢶⣖⠆
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠭⠠⢉⡡⡨⠩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠀⣀⡀⠀⠀⠀⢀⡀⠀⠀⠠⠀⡠⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣻⣯⡟⠋⠑⢠⣤⠄⠒⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠞⠭⢭⢿⠯⢑⡿⣿⡗⠺⢙⣔⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠒⠛⢋⠥⠖⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⡄⠀⣠⡶⠛⠛⠷⣤⠀⠀⣿⠀⣿
⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⢸⡇⠘⣇⢰⡏⠀⠀⠀⠀⢸⡇⢸⡇⢰⡏⠀⠀⠀⣠⣤⣤⣄⡀
⠀⠀⠀⢠⡟⠁⠀⠀⠙⣷⠀⠀⠀⣿⠀⢿⡈⢷⡀⠀⠀⢀⣼⠃⣾⠀⣾⠁⠀⠀⣾⠋⠀⠀⠈⢻⡄
⠀⠀⠀⠸⣧⠀⠀⠀⢀⡿⠀⠀⠀⢹⡆⢸⣇⣀⣙⣛⣛⣋⣁⣰⡏⢠⡟⠀⠀⠀⢿⡀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠈⠻⠶⠶⠛⠁⠀⠀⠀⠈⣷⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⣸⠇⠀⠀⠀⠈⠛⠶⠶⠟⠁
⠀⢀⣀⣤⣴⠆⠀⠀⠶⣤⣤⣀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣤⣤⠶⠀⠀⠰⣦⣤⣀⡀
⣰⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻
⣿⠀⢠⡄⠀⠀⠀⠀⠀⠀⢠⠀⢈⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡁⠀⡄⠀⠀⠀⠀⠀⠀⢠⡄
⢻⡆⢸⡇⠀⠀⠀⠀⠀⠀⣾⠀⣼⠇⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇⠸⣧⠀⣷⠀⠀⠀⠀⠀⠀⢸⡇⢰
⠀⠻⣾⡇⠀⠀⠀⠀⠀⠀⣿⡾⠋⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇⠀⠙⢷⣿⠀⠀⠀⠀⠀⠀⢸⣷⠟
⠀⠀⢸⡇⠀⠀⢠⡀⠀⠀⣿⠀⠀⠀⠸⡇⠀⠀⢠⡶⢶⡆⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⢀⡄⠀⠀⢸⡇
⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⣷⢸⡇⠀⠀⣸⠇⠀⠀⠀⢿⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⣿⠀⠀⢸⡇⠀⢀⡗⠀⠀⠀⠀⢻⡄⠀⠀⣿⣼⠁⠀⠀⣿⠀⠀⠀⠀⢸⡀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⣿⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⢿⣿⠀⠀⢰⡏⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⣿
⠀⠀⠀⣿⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⣷⠀⠀⢸⡿⠀⠀⣸⠇⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⣿
⠀⠀⠀⢸⡆⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⢿⡀⠀⠸⠇⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⢰⡇
⠀⠀⠀⢸⣇⣀⣸⣇⣀⣼⠇⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣠⡏⠀⠀⠀⠀⠀⠸⣧⣀⣸⣇⣀⣸⡇
⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣯⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠈⠉⢉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⢷⣤⡀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⢄⡀⠀⠀⠙⠷⣶⣶⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠢⣤⣀⠀⠀⠙⠻⠷⠶⠶⢾⣿⣿⣿⡿⠛⠉⠙⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⣀⠀⠀⠉⠛⠛⠻⠷⠶⠾⢿⣿⣿⣿⠏⠀⠀⣀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠉⠛⠿⠶⢶⣶⣶⣶⣶⡾⠿⢛⣿⠏⠀⠀⣸⣿⣇⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⣀⣠⣤⣤⣴⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⠿⠟⠛⠉⠉⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢻⣿⡏⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠉⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⡿⢿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣇⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠻⣷⣦⣶⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄
⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠋⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠈⠻⢷⣦⣤
⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠈⠙
⠀⠀⢠⣿⣯⣤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠛⢛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈
⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠶⠶⠶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⢀⣠⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠈⠙⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉
⠉⠉⠉⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟
⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⣰⡟⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⢀⣀⣤⡴⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠞⠭⠉⣳⡶⣦
⠀⠀⠀⠀⢠⡿⣡⡴⠖⠛⠛⠲⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡇⠀⠐⣿⠁⣹⠆⡿⠒⢲
⠀⠀⠀⠀⢹⣔⠁⢰⡆⠰⣦⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⠃⠀⠀⠈⠀⠂⣸⠁⠀⡼⠒⣶
⠀⠀⠀⢠⣯⢭⠇⣀⠀⢘⡏⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⣠⠄⠀⠀⠀⠀⢰⠇⠀⠜⠀⡰⠋⣷
⠀⠀⠀⠀⠀⢾⠀⠘⣷⠈⠀⠀⠀⠀⠀⠀⠠⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠈⢹⣄⠀⠀⠀⣀⣸⡟⠁⣗⡀
⠀⠀⠀⠀⠀⠈⠳⠶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣀⠐⠛⠁⠀⡘⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢰⡄⢠⠀⢤⠀⠀⠧⠀⠀⠉⠀⠈⣳⣄⣤⣤⠤⠤⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⣰⠞⠃⣾⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠃⣧⠸⠇⠛⠙⠀⠀⣀⡠⠄⠀⠈⠉⠀⢀⡀⠀⠘⠳⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣠⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣼⠀⡰⠖⠟⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⢤⣀⠀⠤⢃⠄⠀⠀⣰⡁⠀⠀⠀⠐⡏⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠠⡀⠀⠐⠊⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠀⣀⣀⣀⣀⡠⣧⠀⠀⢀⠄⡰⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⢴⠁⢀⣀⣤⡄⠄⢰⠞⠁⠀⠀⠸⢃⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠷⣄⠀⠀⢀⡾⣡⠀⠀⠴⠃⢀⣠⡤⠶⠒⠈⠁⠲⢶⣦⣀⣠⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢲⣦⠈⠐⠁⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠀⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠐⠂⠒⠊⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠒⢁⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠃⠀⠢⣀⡀⠀⠀⢠⡼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⢻⠿⠟⢛⣿⡶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠾⢿⡷⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⣤⣤⣤⣀⡴⠞⠻⠶⢚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣠⠋⠀⠀⠀⠀⠘⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢰⠃⠀⠀⠀⠀⠀⠀⢹⢱⡀⣠⣴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⣀⣰⠇⣇⠀⠀⠀⢀⣤⣤⠤⠴⣷⣩⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠭⠷⣒⣛⡫⠥⠴⠲⠶⠦⠀⠘⣯⠴⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣟⣛⣟⣻⣹⣻⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣿⣯⣭⣽⣭⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣯⠙⢣⠀⠁⠰⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢯⡹⢻⣶⢈⣧⣤⣠⡁⠀⠀⠀⠀⠀⠀⠀⡬⠀⡠⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⠞⠂⡁⣀⠨⣤⠄⠀⠀⠀⠀⠀⠀⠀⠰⡗⢸⣗⠻⠻⢣⣅⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⡦⣼⣿⠿⠀⡻⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣿⡏⡃⣔⢀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⣈⣷⢦⠜⢷⡾⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣿⣿⢿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠛⠿⢾⣷⡆⠛⡛⣧⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡿⣛⣿⠎⣭⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢱⢶⣿⡿⠇⢰⠿⣿⣿⡟⢻⡷⢶⡶⢶⣾⣿⣿⣿⣿⣿⢿⣻⣛⢯⣽⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⢲⣤⡧⠃⢁⢀⣾⣻⣿⣗⠺⠓⠘⠙⡹⠌⣽⠶⢞⠭⢿⣭⣵⡦⣤⣯⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠰⣽⣛⣷⢀⣈⣹⢧⡝⣿⣦⡷⠲⡅⠀⣉⠀⠍⣽⣺⠃⢌⣹⣷⣻⢿⡛⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢏⣾⡜⢿⠽⣉⡹⠃⠈⠛⣇⣲⡟⣠⣆⠙⢿⡒⡆⠍⠹⣟⣻⡝⢫⣣⣳⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣌⡛⣥⠶⢸⣌⢧⡡⡄⡨⠍⠳⣉⡠⠝⢋⡘⣃⡀⡼⢰⣏⣸⡓⣬⣟⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣹⠷⢶⡎⡓⠇⣹⡙⢁⡙⠆⠸⠁⠌⠓⣺⣇⣡⣧⣹⣤⢿⣿⣿⣉⠛⢽⣶⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣮⣿⢊⣻⠠⠤⡓⣐⠶⠽⠼⢦⡌⣹⣤⣿⣷⣟⣿⣿⣾⠟⠍⠨⠁⠄⢹⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣧⣹⡹⠦⠄⡻⠘⣆⢀⣉⠉⣻⣿⠿⢿⠿⠿⠟⠋⠁⠀⠀⢀⠒⠀⢐⣻⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄⡤⠮⠝⢡⡘⠿⢿⡄⡅⠈⠓⠄⢀⢣⠀⢀⣀⠈⢀⣀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⡶⣦⣮⣥⡴⠄⠲⢃⣁⢀⠒⠊⠻⠇⠠⠬⢌⢆⣹⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣴⢶⠪⣽⡟⠓⣤⡔⠀⠘⠃⣘⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⠿⣿⠿⢿⣿⣷⣆⡒⣀⣶⣶⣦⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⢀⠙⠂⠀⠙⠻⣿⣿⣏⣥⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠰⠀⡙⠀⠀⠀⠀⠀⠀⠉⢻⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠠⠃⢠⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠶⣶⡶⣠⣶⡟⠉⠋⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢀⡈⣻⢏⡼⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠁

⠀⢠⡞⠛⢷⡀
⠀⠀⣷⠀⠈⣷⣄⣀
⣴⠛⠁⠀⣾⠁⠀⠉⠙⠛⠲⠶⠶⠶⠶⠶⠚⠛⠛⠛⠛⠛⠲⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠛⠶⠶⠚⠛⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠈⠙⢦⣀⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⢀⣀⣴⠋⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠈⠉⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠈⠉⠉⠙⠛⠉⠉⠉⣹⡆⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠙⠁⠠⠴⠇⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠙⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣽⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣥⣤⣤⣤⣴⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠳⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠿⣿⠿⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡷⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣶⡶⠶⠆⠘⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡗⢻⣟⡀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⠆⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠄⠀⢀⣀⢀⠘⠀⠀⠀⠀⠀⢠⣿⣿⠍⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣶⣶⣿⠟⠃⠀⠀⠀⠀⠀⢸⣟⣿⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠁⠀⠀⠀⠀⡆⠀⠀⠀⢸⣿⣿⡅⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⡀⠀⠀⠀⠀⢀⠀⠀⠀⢸⡇⣿⣧⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣥⠀⠀⠀⠀⠈⠀⠀⠀⢸⣇⣾⣿⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣬⣷⠀⠀⢀⣀⠐⢦⣤⣼⣿⣿⣿⣿⠷⡤⢾⣇⠀⠠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠓⣶⣿⣶⣿⠿⠈⠀⠀⠀⠀⣰⣬⣭⣴⣶⡞⠁⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⢉⡀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⡏⣀⡀⠀⠀⠀⠀⣤⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⡗⠙⠁⠀⠀⠉⠉⠙⠋⠉⠉⠀⠀⠙⠀⠀⠀⢰⣿⣿⠿⠀⠲⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⡀⠄⠀⣰⣦⢀⣴⣿⠟⠁⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣧⠼⠋⠀⠀⠀⠀⠀⠀⠀⡠⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⠀⠀⠻⣦⣶⣦⣴⣶⣶⣾⣿⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⢀⣀⣼⠇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠛⣋⡉⠉⠉⣾⠏⠀⠀⠀⠀⣸⣦⣶⣾⣿⡋⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⠃⠈⠉⢳⢀⣼⠋⠀⠰⠀⠀⣠⣿⣿⣿⣿⣿⡿⠓⢠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⡇⠀⢀⡴⠋⣸⣇⣠⠾⠅⢀⣴⣿⣿⣿⠻⠿⠏⠀⠀⢰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡄⠀⠐⠒⠀⠀⠀⣠⣼⣿⣿⣿⣿⣦⣭⣤⣾⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠛⠛⢻⣶⣿⣿⣿⣿⠟⠹⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⡁⢸⡿⠿⠟⠋⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⠉⠙⠛⠛⠛⠋⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠋⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠘⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢞⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠸⣿⣻⣿⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⢽⣿⣿⣿⣽⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢷⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡪⠽⣿⣿⣿⣯⡔⣀⡀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣸⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡐⠻⡿⣿⣽⠾⣋⣴⠆⡀⠀⠀⠀⢀⣤⣿⢡⡄⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⢻⣷⣾⣯⣵⡾⣋⣠⡾⢀⣼⡣⢁⣾⠃⠀⠀⠀⣈⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣦⡿⣿⣿⣷⣿⣿⣯⣶⣿⣿⣥⡿⣯⣴⣶⣾⠷⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣏⣹⣿⣿⣿⣿⣿⣿⠿⠋⠙⢻⣿⣿⡯⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠙⠋⠿⠿⣟⣋⠁⠀⠀⠀⠈⢱⣬⣁⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⣶⣶⡾⢿⡏⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠾⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣿⣿⡷⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣻⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⢬⣿⣿⡆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣭⣽⡯⠅⠀⠀⠀⠀⠀⠈⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠟⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢠⣿⣧⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣗⢀⣿⣿⣿⣇⢐⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡾⠸⢿⢿⢿⠿⠸⣟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⣤⣿⣿⣿⣧⣄⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠐⣻⣮⢻⣿⣿⢫⣾⡓⠀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⣿⣿⣧⣝⣥⣿⣿⡇⠀⢸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠛⣧⣀⣼⣿⣿⣿⣿⣿⣿⣄⣠⡟⠻⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠹⣿⣿⣿⣯⣿⣿⣿⡿⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡿⠁⠹⡿⠛⠁




⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠲⡄
⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⡰⠁⠉⠠⠐⠚⠯⣍⠛⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢠⠇
⠀⠀⠀⠀⡇⢠⠀⠀⠀⣤⠀⠈⣧⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⡾⢳
⠀⠀⠀⠀⠘⠧⣄⠀⠘⠟⠀⠀⡜⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢈⡄⠀⢠⠴⠊⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠶⠶⠶⠒⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡞⡆
⠀⠒⠒⠁⠀⠀⢀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⢀⠄⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⣀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡆⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⠀⠀⠀⣿
⠀⠀⠀⠀⠓⠒⢨⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢶⣋⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡷⠀⠀⡟
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡇⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠸⣤⠆⡀⠀⠀⠀⠀⡄⠀⠀⠀⠑⠛⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡄⠀⠀⡦⠃⠀⠀⠀⠀⠀⠀⠙⠢⢀⠗⠒⠲⠤⠴⠒⠒⠒⠉⠀⠀⠀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠶⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡗⢲⠒⠒⠒⠒⠊⢹⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢧⣀⡀⠀⠀⢸⡆⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠒⠈⠀⠀⢀⡠⢭⡵⠤⠜⠁⠀⠙⠒⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠁⠂⢉⠃⠀⠁⠀⡳⢂⠤⠰⠄⠀⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠘⠋⠀⠀⢮

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠠⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢈⣀⠀⠀⠀⣶⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⣛⣠⣿⠛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠆⠀⠀⡀⠀⠀⣀⢀⣴⣶⣿⡿⠄⠀⠀⠀⠀⠈⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠈⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠈⠿⠋⠁⠀⠀⠀⠲⣆⠁⠀⠀⠀⠀⠀⢀⣀⣸⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⠀⠀⠀⠀⠀⢰⠄⠄⠀⠀⠀⡄⠀⠀⠀⠀⢀⡀⠉⢹⡏⠉⠁⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⣷⣦⡀⠀⠀⢠⣿⠃⠀⠀⡀⠀⠀⢀⡠⠎⠀⠀⠑⠄⠀⠁⠀⠀⠀⠀⠘⠁⠀⢸⡇⠠⠰⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⠤⠄⠼⢤⠦⠤⠤⣤⠄⢠⡀⠀⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⣿⠀⠀⣀⠠⠄⠉⢀⣠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠷⢀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣵⣿⡶⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣷⡀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡂⠀⠀⠀⠘⣷⡄⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢿⠿⠿⠿⠿⣿⣿⣿⣿⣦⡈⢻⣦⠀⠀⠀⠀⠀⠀⣿⣿⠟⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣿⣦⣀⠀⠀⠀⠀⢻⣿⠀⠀⠀⢠⣾⠁⠀⠀⣀⣤⣶⣦⡴⠄⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣷⣶⣦⣤⣼⣿⡀⠀⠀⢸⡟⠀⠀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⠉⠀⠀⠀⠈⠉⠙⠛⠻⣶⣦⣼⣷⡀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣬⣿⣿⣷⣾⣿⣆⠀⠀⠀⠀⠀⠀⡀⠀⠈⢀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠛⠁⠀⠀⠀⠀⠀⠈⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣦⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣿⣿⣦⣄⣠⡛⠳⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠓⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡆⢸⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠰⠊⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡅⠀⠀⠀⢠⣿⡇⠸⠇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠀⠀⢀⣠⣤⣄⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⢸⠇⠲⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⣀⣼⡁⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡹⠃⠀⢠⣿⣿⣿⣯⡙⠀⠙⢿⣿⣿⣿⣿⠃⠠⠀⠀⠀⠀⢀⡦⠰⣿⠆⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡞⠁⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣟⣥⡴⠋⠁⠀⢀⣿⣿⣿⣿⣿⡇⠀⠐⠀⠉⠻⣿⠛⠓⠀⠀⠂⠀⣤⠎⠁⠂⣽⣶⡆
⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡏⠀⠂⠀⠀⠀⠀⠈⠉⠉⠒⠉⠁⠀⠀⠀⠀⠈⢹⠇
⠀⠀⠀⠀⠈⢻⣦⡀⠠⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠀⠀⠀⠌⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠹⣷⣶⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⠀⠀⠀⢰⠗⢀⠀⢠⡄⠀⠀⠀⠀⠄⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⢹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠉⠈⣧⣔⣀⡀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣶⠈⣻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⡄⢀⣴⣾⣿⣏⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⡃⠈⠿⠿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⡽⠛⢛⣿⡷⣿⣿⡟
⠀⠠⠤⣴⣤⣄⡀⠀⠀⠀⠀⣾⡟⠀⠇⠀⢰⡄⠀⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⣎⣹⣷⣿⠋
⠀⠀⠀⠀⠉⠻⣿⣦⠀⠀⣸⣿⠁⠐⠀⠀⠸⡇⠀⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⣼⠆⢀⣻⡅⣼⠁
⠀⠀⠀⠀⠀⠀⠈⢿⣇⣠⣿⡇⠀⠀⠀⠀⠀⠻⣄⢀⣄⠙⠀⠋⠉⠁⠉⠈⠉⠑⠆⠉⠙⠂⠉⠉⠈⠉⠁⢠⣤⡄⠘⠋⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠀⣀⣴⡆⠀⠀⠀⠀⠛⠈⠿⠓⣶⢴⡆⢠⡀⠀⠀⣀⠀⠀⢘⡀⠠⡧⠴⠆⠁⡸⠏⠃⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡾⠟⠛⠃⠀⠀⠀⠀⠀⠀⠙⠀⡤⢠⠀⠈⠁⡀⠉⠉⠉⠈⢉⠁⠀⠀⢠⡄⠞⠃⠀⠀⠀⠁⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠃⠀⠂⠀⠃⠘⠀⠘⠃⠀⠀⠀⠀⠀⠠⠂⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠹⡆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⠠⠈⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠈⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢀⡀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣦⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


⠀⠀⠀⠀⠀⠀⠰⠂⣶⡄⢴⠆⢠⡆⢰⡄⢰⡆⠲⠀⢰⡆⢲⣦⢰⡆⢰⣦⠰⠶⠀⠐⠆⢠⡦⢴⡆⠲⠀⠰⡆⢰⡦⠰⡆⢴⠀⡆⠀⢶⡶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠸⠇⠸⠀⠈⠀⠟⠀⠽⠂⠙⠀⠇⠈⠟⠀⠀⠸⠂⠀⠟⠀⠿⠀⠿⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡀⢀⣄⠀⣠⣀⣀⡀⢀⡀⢀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠻⣏⠙⠛⣿⠋⠈⣿⠛⠛⣿⠙⡯⢉⣿⡿⢻⠏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣾⣷⣶⣷⣶⣶⣿⣶⣷⣿⣷⣶⣾⣿⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⢡⡄⢬⠟⡣⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠰⣔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢁⠀⠙⠳⣟⣻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠰⠎⢆⠘⢆⠐⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⢠⠰⡀⢀⢢⠀⢃⢀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⢤⣆⡁⠪⠍⣉⡿⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣇⠑⠆⡄⠤⡴⣺⡄
⠀⠀⠀⠀⠀⠀⠀⠈⡌⠀⣌⢹⡃⠾⣻⠡⣷⡗⣁⣶⠀⢠⣤⢠⣤⠠⣎⣩⣇⢅⡟⢗⡛⠴⡍⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢙⡳⠖⡅⢿⠛⣦⠟⣺⠒⣭⢶⠁⡺⣅⠹⢶⡤⢿⠽⠨⡒⠫⠒⡖⢁⠗⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡉⠳⢯⡉⡕⢈⣉⡉⠽⣴⢸⡖⢚⣳⡟⣠⡝⢻⡖⣾⣈⡙⠓⡶⠗⠪⢋⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢨⣵⡉⠛⢩⣘⢒⠖⠦⣴⣨⣽⣂⢽⣫⡁⠷⣬⡟⡩⢀⢺⡾⣿⣧⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣱⣞⡯⡹⣎⣮⡖⣶⣥⣉⡓⣚⣧⠔⢶⣢⠰⡁⢻⣦⠎⡦⣤⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⡼⠷⠿⣷⣾⣾⡻⠟⠭⠿⠫⠼⠿⣇⣾⡼⢳⣴⠩⣶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣽⣗⣻⢤⣆⣩⣿⠠⡟⠿⠏⣩⠿⢾⣿⣿⣿⣟⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷⣾⣯⣒⣽⢋⣷⣺⣿⣿⣞⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠿⢿⣿⣿⣿⣿⣾⣷⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⢿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠻⠿⣿⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠉⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⢄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣾⡿⠷⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣓⣈⡐⢆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢰⣿⣿⣯⣿⠗
⠀⠀⠀⠀⣠⣤⣶⣶⣿⣿⣷⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠘⣿⣿⣿⣟
⠀⠐⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠳⡭⠊
⠀⢚⣿⣿⣿⣿⣿⣿⣿⣛⢻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣰⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑
⢿⣿⣿⠁⢻⣿⣿⣿⣿⣧⣤⣔⡰⠻⣿⢛⣛⠀⠀⠀⠀⢀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣯⢉⣿⣿⠃⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠈⠃⠀⣸⣿⣿⣿⣿⣿⣿⣿⣽⣿⢟⡿⡟⠀⠈⠀⠂⠀⡀⠂⠄⠀⢄⠀⠀⠀⠀⠀⠀⠛⡠⣼⠇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠁⣾⡄⢠⢤⣾⡇⢠⡴⡎⣿⣥⣺⢄⣠⣰⠆⣃⣬⠁
⠀⠀⠀⠀⢻⣿⠿⢿⡿⠟⣿⣿⣿⣿⣿⣿⡊⢁⣳⣿⣿⡟⣟⠸⢷⣧⣽⣷⢟⢫⡩⠼⢫⣴⠟
⠀⠀⠀⠀⠀⠻⠀⠀⢧⠀⠾⠋⢹⣿⣿⣴⣳⣿⣿⣿⣃⠀⠈⡷⢾⣯⣻⣛⣛⢁⡀⢖⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠹⠿⣿⣿⣿⡿⢓⣤⢞⣡⠄⢀⣹⣻⡋⣀⢡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣟⡻⣝⣚⣭⣷⣾⣿⣿⣿⣿⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠊⢳⣄⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡄⠀⠑⣾⠀⠀⢋⣿⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠾⠟⠒⠦⠤⠾⠁⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣶⣷⣤⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⠿⠿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠽⠖⢤⣼⡿⢿⣿
⢠⣤⠶⠶⢶⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⡈⠛⠁⣠⣞⣲
⠀⠉⠛⢶⣾⣿⣿⣿⣿⣿⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠐⢻⣿⣦⣿⣿⡅
⢸⣏⢉⣿⣿⣿⣿⣝⢿⣿⣷⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⢀⡽⢿⣿⣿⣿⣿⣿⣷⣭⣻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⡄⠀⠀⠀⠀⠀⢀⠀⢼⣿⣿⣿⡿
⠘⢳⣶⣿⣿⣿⣿⣯⣤⣴⣬⣍⠛⠹⣧⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣴⢿⣿⣿⡀⢀⠀⠀⠀⢀⣿⡂⠈⢿⣏⠉
⢿⣉⣿⣿⣿⣿⣟⣩⡤⠄⠀⠈⠀⢦⣽⣿⣦⣴⣶⡿⣿⡿⠛⠿⠛⠉⠉⠉⠁⠁⠸⠿⡿⢻⣯⣠⠀⣠⡿⢙⣧⠀⠀⣿
⢴⠟⣋⠍⣼⣿⠋⢁⣀⣤⣤⣤⠄⠀⠉⠛⠛⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⠻⣿⣿⠇⠈⣿⡆⢀⣹
⠈⠛⣷⣾⣿⣿⡿⣻⣽⡿⠃⠀⢀⡞⠁⠀⣠⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠘⠀⠀⠀⢹⣿⣿⠟
⣟⠻⣿⣿⣿⣷⣿⣿⣯⡶⣤⢀⡟⠀⠀⣼⠁⠀⠀⣾⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠈⠛⠾⠿⢿⣿⠿⣫⣿⣿⡟⣼⠃⢀⡄⡇⠀⠀⠀⡇⠀⠀⡞⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁
⠀⠀⢿⣻⣿⣿⣿⣿⣿⡿⣼⣿⢣⣾⠀⣷⡄⢠⣦⡇⠀⠀⡇⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⡇⡇⣇⣿⣠⣷⣾⣿⣿⣏⣉⠀⡷⠖⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣴⣿⣿⣿⣿⣿⠟⢉⣨⣿⠿⠿⣿⣿⣿⣿⣇⣠⣆⠀⠀⠀⠀⠀⣀⣴⣟⣀⣴⣿⠇
⠀⠀⠀⠀⠀⠀⢰⡏⣿⣿⣿⣿⢛⣽⣿⣷⣾⣯⣭⣴⠶⢞⣯⣽⣍⣉⠉⠁⣙⣷⠶⠶⢛⣿⣿⣿⡿⣻⣿⠏
⠀⠀⠀⠀⠀⠀⠘⣇⣿⣟⣈⠻⠮⠯⡉⠋⠉⢹⣅⣤⡴⠹⠿⠿⢻⣿⣿⣿⣯⣿⣟⣿⡿⢋⣽⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣞⡀⢀⠀⠀⢈⣿⡋⠀⠀⠀⢠⠾⠛⡉⠙⢻⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢿⣿⣿⣿⣿⣿⣿⣧⡀⢀⣠⣄⣴⠞⠀⢠⠁⠼⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣾⣿⣿⣶⣝⣻⠛⢛⠋⠹⣦⣶⣿⣿⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿⢿⣾⣿⣷⣴⣦⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠈⠈⠙⢿⡫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣬⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠉⠛⣗⢘⣶⣶⣴⣶⣦⣤⠄⢀⣀⣀⣬⣯⣽⣶⣶⣾⠷⢶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠿⠿⣯⣙⠛⠋⠉⠉⠀⠀⠀⠙⠿⠋⠓⠦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣤⣿⣿⣿⣿⣤⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⠿⠿⠿⠟⠛⠛⠻⠿⠿⠿⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠺⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠟⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣀⡀⠀⠀⢀⣀⣤⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣯⣽⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⢀⣠⣀⢹⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠈⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⣶⡬⠉⠉⠀⢀⡙⠄
⠀⠀⠀⠀⠀⠀⠿⠅⢁⡀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠻⣿⣶⣾⣿⣿⠛⠛
⠀⠀⠀⠀⠀⠀⠘⠧⣄⢀⡄⠀⠂⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⢫
⠀⠀⠀⠀⠀⠀⠀⠲⢿⣿⣿⡶⠆⠀⠶⠆⠲⠀⠀⠛⡻⠷⠶⠶⠢⠤⠤⢀⣀⣀⣀⣀⣀⣀⡤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠹⣄⡀⠀⠄⠀⠀⢠⠸⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣨⠷⢦⣤⣈⣙⠂⠀⢤⣠⣼⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣽
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣤⣉⡙⠓⠀⠐⣿⠋⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣏⣓⠀⢠⣾⠂⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣀⠼⠗⠀⢶⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⡖⠀⠈⠳⡦⠀⠀⡠⠔⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⠴⠚⢷⣖⠊⢀⣀⡀⠀⠀⠂⠀⠀⢀⠀⢀⡤⠄⠀⠀⠀⠀⠀⠀⢀⡄⠠⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣣⡀⠀⠀⠀⡉⠉⢉⠈⠉⠉⠀⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⠉⣮⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡅⡠⠊⢈⠁⠀⠢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣯⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡤⠂⠀⠀⠀⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⣤⡶⠙⣾⠻⠀⠀⠀⢀⠀⠀⠀⠔⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣾⣧⣀⡶⢠⣶⢀⠈⠀⠈⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣶⣷⣿⣄⣤⣤⣤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡈⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠈⢿⣿⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠀⠃⠀⠀⠀⢀⣠⣿⣿⣦⣜⣿⣷⡄⣀⣀⠀⠀⠴⠀⡀⠀⠀⢠⡜⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⢀⣀⣑⣢⡀⠛⣿⣤⣤⣤⣈⣉⣉⣠⣠⠿⠿⠛⠻⠷⣿⣿⣷⠶⠶⠾⠷⠄⠰⢾⣧⡰⡥⠀⠀⠠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠷⠀⠼⠛⠛⠣⠛⢿⣿⡷⠄⡀⠀⢿⡦⠀⠀⢍⠉⠀⣄⠀⢰⣰⣴⣾⡷⢳⣷⣶⡭⢿⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠒⠻⠃⠀⠉⠙⠛⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣦⠀⡰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠺⠀⠷⠁⣧⢺⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⣆⠀⠀⠀⠁⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣋⠀⠀⠈⠳⣤⡀⠀⠀⢠
⠀⠀⠀⠀⠀⡎⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠐⢻⣯⠀⠈⠰⣶⠆⢉⡷⠒⢇
⠀⠀⠀⢀⣀⣱⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢉⣧⠀⠀⠠⠠⣀⡼⠧⣤⢤
⠀⢀⣄⢸⠀⠙⢧⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠚⠹⣧⡄⠀⣰⠁⠀⠀⣿
⠀⢸⡌⠳⣇⠀⠈⢣⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠋⣴⣠⣟⠓⠶⠞⠁
⠀⠀⢣⠀⠙⠂⠀⠀⢳⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢹
⢸⠁⠈⠁⠀⠀⠀⠀⠀⠻⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⣇⣸⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠇
⠈⢆⠀⠀⠀⠠⠀⠀⠀⠀⠹⡖⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⠁⠀⠀⠀⠿⠁⣧⠋⡇⠀⣠⠀⠀⠀⠀⢸
⡤⣌⣆⠀⠀⠀⠀⠀⠀⠀⣖⡛⢦⣘⠢⠤⠤⠤⢶⣔⡒⠂⠴⠤⠤⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠚⢹⣀⣤⡀⠀⡆
⠱⡀⠙⢧⡀⠀⠀⠀⠀⠰⣂⠛⠶⢬⠓⠀⠀⠀⠀⠀⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢘⡇⠀⣆
⠀⠙⣄⠀⠳⣄⠀⠀⠀⠀⢠⡛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⢨⠷⣆⡾
⣄⠴⠾⢦⡀⠈⠀⠀⠀⠀⠀⡬⣟⣛⣛⣥⠀⠀⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⣩⠽⠶⠷⢦⡀⠀⠀⠀⠀⠀⠙⠉⠉⠈⠉⠁⠉⠀⠀⠀⠀⢀⣠⠤⠔⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠙⠒⠂⠀⠀⠈⠓⠤⣄⡀⡀⠀⠀⣀⣀⣀⠠⠤⠄⠀⠀⡀⠈⠀⢀⡀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣸
⠀⠀⠀⠀⢆⣀⣀⣀⡤⠴⠊⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡽⠛⠋⠉⠁⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⠏
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠦⠀⠀⠀⣀⣀⠤⠀⠈⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⣀⠴⠃⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⡥⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣲⠖⠒⠊⠁⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢤⣀⡀⠀⠀⢀⠫⠤⠤⠤⢤⣀⣀⣀⣀⠠⠤⠤⠔⠒⠒⠛⠉⠁⠀⠀⠀⢰⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡈⠉⠑⠚⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣄⡀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⠤⣀⠤⠛⠲⢄⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢰⡀⠀⠀⠈⢧⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢧⠀⠀⠀⠈⠳⣤⠤⢤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠘⡄⠀⠀⠀⠀⠘⢆⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠄⠘⢶⠲⠿⢿⣦⣬⣆⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠉⠉⠓⠢⠽⣻⣅⠀⠀⠈⢧⠀⠳⡀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⢀⣤⢷⡀⠙⠿⢟⣉⡭⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠁⠒⠒⠛⠺⢦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠤⠤⠤⠤⠖⠚⠉⠉⠉⠉⠲⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢀⡆⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⢰⡋⠀⠀⠀⠈⠋⠿⢠
⠀⠀⠘⢶⣌⣉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⠶⢦⣤⣀⣀⣠⡴⢞⡿⠓⢦⣀⠴⠊⠉⠉⠉⠙⠦⣄⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠈⠙⠛⣻⠃⠀⠀⠀⠀⢀⣼⡿⣡⣾⣋⠁⠁⠉⠙⠛⠉⢠⣯⣶⣶⣶⢿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⠤⠽⢦⡀
⠀⠀⠀⠀⠠⠄⠊⢁⠀⠀⠀⠀⠀⣼⣿⢁⣯⣶⣾⡅⠀⠀⠀⢀⣴⣿⣿⣿⣿⣏⠀⠀⢀⠤⣶⣶⢶⡦⢤⡀⠀⠀⠈⡍⠙⣯⠐⠂⢄⡀
⠀⠈⠳⠶⠶⠶⠞⣿⠀⠀⠀⠀⢰⣿⡇⢀⠙⠯⠟⣡⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡆⢀⣀⡀⢷⣭⣪⠅⠀⠀⡀⢀⡠⠴⠚⠓⠒⠒⢤⣑⡄
⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⢀⣿⣿⡇⠸⡄⠐⠚⠁⠀⠀⠈⢿⣿⡯⠭⠬⣭⣿⣷⡀⠀⠈⠙⠁⠀⠀⠀⣌⣠⠀⡀⠳⣾⣯⡀⠀⠀⠈⠁
⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⢀⣾⣿⣿⠁⢰⡇⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⣀⣤⡬⢽⢿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠙⣿⣷
⣀⣠⣴⣿⣿⣤⣤⣤⣴⣾⣿⣿⣿⠛⠀⡌⠁⡀⠀⠀⠀⢀⣠⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⢸⡏
⠈⠙⠛⠿⠿⠿⢿⣿⠿⠿⠟⠋⠁⡀⣰⢿⣆⠙⠿⢿⣿⣿⠇⢸⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢠⠀⠀⢰⠃⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⢸⣿⡆⠀⠀⠈⠿⠀⠘⡆⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠸⠀⠀⠈⢧⣀⠀⢀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⡿⢹⣇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣷⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⢈⠉⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡼⠁⣼⣿⣦⣤⣼⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡀⠀⠀⠀⠀⡇⠀⠀⢀⠈⢧⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠈⠀⢰⡟⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⡀⠀⠀⠀⡇⠀⣄⠈⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢀⡟⢰⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⢷⡀⠀⢠⠃⠀⠙⠀⠀⢦⠀⠘⢦⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠊⢠⡿⢫⣿⠟⣿⣷⣤⣀⣀⣠⣾⣿⣿⣿⣿⣿⣏⠳⠤⠊⠀⠀⠀⠀⡄⠈⠁⠀⠀⠳⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⢠⠟⠁⣸⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣆⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠠⣄⠀⠀⠀⠀⠹
⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠰⠋⠀⣰⠋⠀⣸⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠻⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢹⡄⠀⠘⣆
⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⢠⠟⢀⣿⠻⣿⠿⣿⡏⢻⡿⠸⡟⠘⣇⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠈
⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⣸⠃⢰⠏⠀⣿⠃⢸⡇⠀⡇⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠌⠀⠀⡟⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠋⠻⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠠⣤⣄⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠠⠔⠛⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡾⠀⣶⣄⣀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠈⠀⠈⠉⠉⣿⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠸⣧⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠲⣴⣿⣆⣀⣾⠃⠀⠀⠀⠀⠀⢸⡿⠀⠀⣠⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠰⠶⠛⠛⠛⠉⠙⠛⠻⠛⠛⠛⠓⠶⠀⣾⡇⠠⣾⠋⠀⠈⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⣿⣧⣴⠇⠀⠀⠀⠀⢸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⣸⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣠⣤⣤⣭⣿⣦⣤⣤⣤⣤⣤⡿⠀⠀⠀⠀⠀⢰⡿⠉⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣠⡾⠛⠁⠀⠀⠈⠉⠉⠉⠉⠙⠋⠉⠉⢳⠀⠀⠀⢠⡿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⣠⡿⠀⠀⣠⡿⠁⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠿⣏⠀⢀⣴⠋⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣷⣾⣿⣿⣿⡏⠁⠀⠈⢠⣾⣇⡀⠀⠀⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣝⠻⣏⡻⣧⡀⠀⢰⠏⠀⠈⠁⢀⣴⣿⠏⣽⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢿⣿⣷⣬⡙⠾⠛⠿⣏⠀⠀⢀⣶⣿⣯⡁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⣿⠀⠻⣷⡈⠙⢦⣄⡀⠙⠷⠶⠿⠁⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⣿⠀⠀⢹⣷⠀⠀⠉⠙⠛⠳⠚⠒⠛⠃⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⡄⠀⠀⠀⠀⠀⣠⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢀⣠⣴⡿⠋⣀⣀⠀⠀⠐⠻⠞⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢤⣴⣿⣿⡿⠿⠞⠛⠁⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡏⠀⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠂⡴⠢⠘⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⠂⠄⢀⡀⢀⡄⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⡿⠛⠲⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠎⠀⠄⠛⠀⠂⠀⡀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠸⣿⣿⣿⣇⠀⠀⣤⣽⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠠⠀⢀⡰⠻⠉⠁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢶⣦⠀⠐⢿⡿⠻⣟⡁⠀⠉⣵⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣾⠅⠀⣠⠞⠀⠀⠈⡛⠲⢦⠑⢾⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⠃⡚⣥⣶⣦⣀⣸⣿⣿⡆⣱⠌⡈⢳⡆⠀⠀⠀⠀⠀⠀⠀⢠⡆⢆⣀⣀⡆⣀⣄⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢈⠰⢦⣙⡛⢿⣿⡿⠟⡡⢺⡇⠀⠀⢄⢹⣄⠀⠀⠀⠀⠀⠀⠈⠁⠀⡄⡠⠂⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡄⡀⠈⣿⣍⠶⣄⠀⡰⢣⣿⡇⠶⠀⣿⠀⠹⣆⠀⠀⠀⠀⠀⠀⠠⠠⢀⠀⠈⠀⡌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣷⡀⠞⢪⣿⣧⠈⠻⠁⢸⣿⡿⠀⣴⣿⠀⢸⣟⠂⠀⠀⠀⠀⠈⠁⠑⢊⠈⡀⢃⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡄⠹⣷⣦⡈⠻⣿⡆⠀⠀⢸⡟⣥⣼⡿⢃⣆⣸⠙⠳⣄⡀⠀⠀⠀⠐⠚⠙⠈⠘⠘⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣧⠀⣌⠻⢿⠼⣾⣿⣆⠀⣾⣿⡟⠈⣀⢾⠈⠹⡄⢠⡀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⠢⣤⡄⠙⡿⠟⠀⠘⢋⡆⡸⠉⠘⠄⠀⠑⠀⠙⢶⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢹⠢⠽⠢⣀⣤⠎⠙⠁⠀⠀⠀⠀⢠⡀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣴⠀⠈⠀⠀⠀⠈⣇⠀⠀⠀⠀⠢⣀⠀⣸⢻⡓⢤⣀⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠿⢹⡄⠀⡰⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠓⠃⠀⠙⢆⠘⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠳⠋⠁⠀⠀⢢⡀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣠⠆⠀⠀⢀⠀⠀⠀⠀⠀⠙⠶⠋⠀⠀⣶⡀⠀⠀⢀⡏⣟⠲⣴⣄⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠿⣄⣀⡴⡿⣧⠀⠀⢀⠀⠀⠀⠀⠀⡼⠋⠙⢦⣄⡾⠁⠀⠀⠀⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠉⠁⠀⠁⠈⢧⡤⠊⠀⠀⠀⠈⠾⠁⠀⠀⠀⠈⠁⠀⠀⠀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣴⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣤⡍⢉⡍⠉⠉⣩⠉⠉⠉⠉⣨⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⡴⠃⣼⢁⡀⢀⡄⢀⣤⡀⢰⠇⡄⢀⣤⡀⣠⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⣰⡟⣼⠃⣼⠁⣿⡀⢀⡿⣾⠁⣿⡴⢁⡿⢡⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⣤⠞⠁⠉⠀⠈⠉⠈⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠁⠈⠁

⣿⠿⠿⠿⡿⣟⠿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡁⣿⣧⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣧⣥⣾⠫⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⣟⣽⣿⣿⣽⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⢉⣲⣦⡤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣻⢿⡼⡿⣙⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⡟⠛⠻⣿⣿⠿⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣿⣟⡿⡗⣻⡽⠷⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⢋⣤⡤⠤⠀⠈⠙⢿⣿⣿⣿⣿⡄⠀⠀⠙⢿⣧⡀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢷⡿⣷⣯⣹⣿⣹⣻⣶⠀⠀⠀⠀⠀⠀⠀⣸⡿⢁⡤⠛⡡⠴⠶⠶⠾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡶⣿⣍⣻⣷⡻⡟⣽⣾⡇⠀⠀⠀⠀⠀⠀⣿⣱⡿⣷⣼⣿⣟⠛⠓⠀⠈⠉⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣡⣟⣨⡷⢽⣖⣬⣺⡿⠿⣄⠀⠀⠀⠀⠀⣿⣾⣿⣷⡻⠞⡿⢧⡈⠶⢦⣄⣠⣸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⣿⣿⣾⣽⣿⣿⣢⣻⣿⣷⣶⣦⣴⡾⣿⡟⢻⣻⣏⢣⣿⣿⡙⡱⠦⢹⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡉⣿⢿⠶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣯⣏⢁⣪⡛⠛⡿⢿⣾⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣫⣷⣸⣶⣾⠻⢋⣿⣿⣿⣿⣷⣿⣿⣿⢿⢻⣾⣿⣿⣿⣅⣊⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣵⡿⠯⠽⣿⣿⣿⣿⣿⣿⣿⣬⢿⣿⣞⢻⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣟⢯⣛⣲⣾⣿⣿⣵⣿⣻⣿⣿⢿⣿⣯⣿⣷⡟⠛⣀⣀⡀⠀⡀⠀⡀⠀⢀⡀⣀
⠀⠀⠀⠀⣀⡀⢀⡶⠀⣀⣀⡜⠀⢀⡀⠆⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢻⣿⣿⣿⣿⣿⣿⡿⠃⠟⠛⢻⢿⣿⣿⡀⠀⠀⠀⠚⠹⢦⡀
⠀⠀⠀⠀⠙⠋⣸⠞⣡⣿⣿⣿⢿⣷⣤⡀⠈⠑⢀⠀⠙⢿⣯⣳⣽⣿⣿⣿⣿⣿⣿⣿⡯⠝⠚⠻⣿⡿⢿⡿⣋⠴⠂⠀⠹⠒⠌⠋⠻⡿⠷⠆⢦⣬⢟⣿⠢
⠀⠀⠀⠀⠀⠀⠈⠀⠘⠟⠟⠈⠃⠙⠋⠓⠀⠀⠀⠀⠀⠀⠈⢶⣹⢹⠙⣿⣿⣿⣿⣿⡿⠛⠀⠀⠈⠀⠀⠉⠁⠀⠀⠀⠀⣄⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⣧⡠⢿⠉⠉⠉⠁⠀⠀⠀⢀⠀⢀⡀⠀⠀⠴⡾⣤⣉⣻⢿⣷⣶⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⢹⣸⠀⠀⠀⠀⠀⢀⡀⠀⡠⢒⣙⡲⣤⣤⣶⣿⣛⣯⣿⣝⣿⣟⣱⠾⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⢀⣀⠀⣿⢠⡀⣴⡄⣽⣍⣉⣿⣿⣿⣿⣿⣫⢿⠿⠿⠿⠿⢿⠿⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣶⣶⣶⣶⣤⣀⡀⠀⠀⠀⠼⠟⠛⠛⠉⠉⠁⣯⠽⠛⢋⣩⣽⣾⣿⣿⣿⡿⠿⠟⠉⠁⠀⠀⡀⠀⠐⠲⠤⠃
⠀⠀⠀⠀⠀⠀⠚⠒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡤⠀⠀⠠⠀⠀⢠⢼⣇⣤⡶⠾⠟⠛⠛⠉⠉⠙⠆⡀⠀⠦⠄⠰⠀⠀⢀⠝⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣉⣿⣿⣿⣟⣉⣁⠀⠀⠀⠈⣁⡤⠛⠛⠈⠙⠒⠀⠀⠀⠀⣀⣁⠠⢀⡀⠀⠀⠀⠀⣈⢁⣀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠉⣉⣻⡿⢟⣛⠛⠛⠉⠉⢳⣤⣀⠀⠀⠀⠁⠀⠀⡀⠀⠤⠴⠀⠀⠀⠀⠀⠂⠀⠚⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠈⠉⠁⠀⠀⠀⠀⠀⠙⠀⠀⠀⠄⠀⠀⠀⢀⡀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⣶⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⢸⡏⣹⠅⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠙⠋⠛⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠃⡄
⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠈⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⣤⠴⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⢀⠌⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡅⣀⡇⠀⠀⠀⠀⠠⣴⠄⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠔⢁⡠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠑⠚⠀⠀⢀⠀⣰⠔⠊⠀⠀⠈⠒⠚⠺⠶⠵⠀⠀⢀⠀⠀⠀⠂⢁⠄⠋
⠀⠀⠀⠀⠀⠀⠓⠛⠄⠒⠤⠄⠓⠔⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⡀⠔⠉⠸⠀⠐⠊⢁⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠉⡤⠔⠊⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠡⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⡄⠔⠂⠄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠤⢀⣀⠀⠂⠀⣔⠒⠒⠛⠉⠒⣒⠆
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠭⠡⢉⡡⡌⠭⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠀⣀⡀⠀⠀⠀⢀⡀⠀⠀⠠⠀⡠⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣻⣯⡟⠋⠑⢠⣤⠄⠒⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠚⠭⢭⢿⠯⢑⣿⣿⡗⠺⢙⣴⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠒⠛⢋⠥⠖⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⣿⣟⣿⣭⡭⢯⣭⣿⣻⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣯⣓⣿⣿⣿⡿⢷⣾⣿⣿⣿⣿⣿⣯⣽⣿⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣿⣶⣿⣿⡷⣟⣵⣿⣾⣯⣾⣿⢿⡿⣳⢿⣿⣿⡽⣧
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠓⢄⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⡀⠀⠀⢠⣿⢟⣿⡿⢿⡾⣿⠟⠷⠋⣽⢿⣿⡷⠻⠟⣿⣻⣾⣿⣶⢻⡆
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⢷⡀⠀⠀⠀⠀⣸⠀⠀⠀⣷⠀⠀⠾⠏⢈⣁⡀⠋⠀⠁⠀⠀⠘⠁⠀⠀⠀⠀⣾⣯⣿⣷⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢱⠀⢀⣠⡼⣧⠀⠀⠀⠀⣿⠀⠀⠀⡟⠀⠀⢰⢠⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣦⣹⡟⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣦⠈⠁⠀⢹⡀⠀⠀⢠⡟⠂⠀⣸⠁⠀⠀⠸⡆⠠⢤⣤⣤⢤⠀⠀⠀⢀⣀⣀⣠⣀⠈⢻⡟⣛⡻⣮⢿⢼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⢀⣼⣇⠀⠀⣾⠀⠀⢀⡏⠀⠀⠀⠀⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠸⠾⣏⠁⢻⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠉⠀⢻⡀⢀⡟⠦⠀⣸⠇⠀⠀⠀⠀⣧⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠈⢧⠾⠁⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⢠⣄⠈⠳⣶⠶⠂⠀⣠⠤⡀⠀⠀⠀⠀⢀⡞⠉
⠀⠀⠀⠀⠀⣤⠔⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⡇⢲⠌⡑⠒⠶⠶⠒⠋⠁⠀⣹⡄⠀⠀⣰⠏
⠀⠀⠀⢀⠼⣇⠀⠀⠀⠠⡄⠀⠀⢀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠹⣌⠢⢄⠀⠈⠀⠈⠀⠈⠀⡼⠁⢀⡼⠋
⠀⠀⠀⣮⠀⠙⣧⠀⢰⡏⠋⣻⠟⠧⣴⠒⠒⠂⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⢷⣄⠈⠡⠴⠶⠒⠂⠉⣀⣴⡿
⠀⠀⠀⠘⢦⡀⠘⢧⠸⡗⠾⠁⠀⠀⡈⢷⣤⣤⡀⠈⡇⠀⠀⠀⣀⣀⣀⣤⠟⠙⠷⣦⣤⣤⣤⠖⠋⠁⠘⡇
⠀⠀⠀⠀⠈⣷⡀⠈⠳⣝⣶⣤⡀⠋⠀⠀⠀⠀⠀⠈⣧⡶⠿⣏⣿⣿⣿⣿⣿⣿⣶⣦⣬⣤⣤⣤⣤⣶⣶⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠹⣟⠢⠤⠞⣿⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣄
⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⣸⡷⣄⠀⠳⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧
⠀⠀⠀⠀⠀⠀⣠⣿⣷⡄⠀⠀⠀⠈⠙⠛⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⣤⣀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢠⡿⣿⣿⡟⢡⣣⢽⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⢛⣟⣻⢛⣿⣋⡛⢻⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣻⣻⣿⣛⣿⣟⣛⣛⣻⣛⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡠⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⠡⠀⠀⠆
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⢺⣏⣤⠄⢰⠆
⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠐⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣡⠀⠘⡛⠷⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠅⠀⠀⠘⠗⠟⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡮⠁⠀⡠⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢮⠀⠀⢨⠀⠀⠀⢠⢹⡇
⠀⠀⠀⠀⠀⠀⢀⣤⢆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⡡⢄⠀⠉⠈⠀⠀⠀⠠⢬⡇
⠀⠀⠀⠀⠀⠀⢈⣙⠯⣝⣿⠀⠹⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠠⠄⠀⠀⠂⠀⠀⠀⠀⠚⠗⣇
⠀⠀⠀⠀⠀⠀⠘⡛⣾⣓⠀⢈⠔⠀⠘⢷⣤⠤⠤⡄⠒⡲⠒⠒⡒⠲⣖⣂⠩⠯⠀⠠⠀⠀⠀⠀⠀⢀⠈⠀⠀⠠⢉⣿
⠀⠀⠀⠀⠀⠀⠀⠘⢿⠁⠀⣈⣠⠄⠲⢛⠀⠁⠊⠉⠰⠒⢀⠀⠩⠔⠨⠆⠀⠀⠀⠚⠀⠠⠀⠀⠀⠀⢉⠀⠀⠠⠘⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⠟⠵⣴⠆⠀⠎⡀⠟⠐⠈⠌⠁⠈⠈⢤⠀⠀⠂⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⡉⠀⢀⠀⠰⠦⣾⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⠶⡿⣈⠀⢄⠀⠀⠀⠀⠰⣀⠀⠒⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠾⣯⣐⣐⠂⠄⣐⠀⢀⢃⠀⠐⠀⠌⠡⠀⠈⠤⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠂⢋⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢠⣽⠭⡋⠛⠃⢁⣴⣏⠈⢠⢃⡖⡀⠀⠀⠀⣀⣀⣀⡀⠃⠀⠉⠀⠀⢁⠔⠢⡖⣀⡈⢂⣤⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣉⡲⣏⣀⠶⢎⣈⣠⣼⣷⠿⢿⣷⠟⢿⣶⡿⢏⠙⠧⠀⠀⠀⠀⠉⢡⠀⡄⠢⢋⡙⡧⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣏⠻⣿⣟⡛⢛⠀⠀⠀⠥⢌⡥⣿⠁⠛⢬⢇⠠⠀⠀⠀⠐⠀⠀⠤⠀⠐⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣦⣿⡆⠀⠀⠐⠀⠀⡀⠠⢄⡀⠁⠠⠀⠦⠐⠀⠀⠀⡦⠀⠄⣸⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠚⠀⠀⠀⠀⠄⠀⠀⠃⠀⠈⡀⡀⢀⠀⡀⣘⠁⢆⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⡅⢀⠀⠠⣤⠖⠤⠀⠖⢀⣂⣁⠀⠀⠀⢠⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠦⣴⣆⠈⠀⠀⠀⡀⠀⠀⠜⠠⣦⢐⠼⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⡿⣶⣁⣌⣼⠺⢾⠍⠛⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣴⣴⣤⣤⣄⣠⣤⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⢸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯
⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡸⠛
⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⢀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⢸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠲⣾⡿⠛⣤⡀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣅⡀⠚⢹⣷⡄⠀⠈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣶⣿⣿⡄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⡉⢹⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠑⠿⣽⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠙⣿⣿⡆⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠛⣿⠁⠀⠀⠀⠀⠀⣾⣿⠟⠀⠀⠀⠀⠀⠐⢻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣴⣿⣆⠀⠀⠀⠀⠀⣿⣄⣠⣤⣄⠀⣤⣄⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⠀⠀⠀⠀⠈⢻⣿⠉⠿⠁⠙⠁⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢿⣄⣠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣴⣿⣷⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⠟⠛⠀⠈⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏⠀⠀⢀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣼⡇⠀⢸⣾⡟⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⢻⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠉⠀⠀⠀⣸⢿⣤⠛⠀⠀⠀⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⠀⠀⠀⣿⡀⠿⠀⢠⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⡀⠀⣀⢸⣿⠀⣶⠀⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣶⣿⣿⠀⠀⠀⠀⠀⠈⠻⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣿⣿⣿⣏⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⢹⣿⠟⠿⢿⣷⣤⠄⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠉⠀⠀⠀⠉⣥⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⣤⣶⣾⠛⠁⠀⠀⠀⠀⠈⠛⠛⠓⢲⣤⠀⠀⠈⠉⠛⠿⢷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⣤⣀⣠⠀⠘⠙⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠇⣼⠟⠁⠀⢀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠀⣤⡀⠀⠀⠀⠀⢀⣠⣤⡀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⣤⠋⠀⠀⠀⠈⢰⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠈⠛⢀⣀⣶⠇⠀⠛⠛⠁⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⣤⣆⠀⠚⠀⠀⠀⠀⠉⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⣰⣶⣤⣿⣿⣿⣶⣦⣤⣶⣤⣄⢀⣤⣾⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠉⣿⡟⠋⢹⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⢹⡧⠀⣿⣿⠆⠘⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⣤⠀⢾⠏⣀⠀⢸⣿⠋⢿⣿⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣿⣄⠀⣀⡨⠆⠸⣿⠄⠘⠁⠀⠀⠀⠀⠀⢀⣿⣦⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢈⣿⣏⠻⠃⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣿⣧⣄⣹⣿⣷⠀⠃⠰⣿⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⡟⠻⣿⠁⠀⠀⢣⣤⣿⠀⢀⣤⣤⣶⣾⣿⡏⠙⢿⣷⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠻⣦⡀⠀⢀⣽⣿⠀⠈⠻⣿⠉⢸⣿⠇⣶⠀⠿⠀⠀⡤⠐⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢀⠈⠁⠀⢼⣿⣧⣄⠀⣿⠁⠀⢸⣿⠀⠉⠀⠀⠀⢀⡀⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⢰⠀⠀⠀⠀⠀⣸⣿⣿⡟⠀⣿⠀⠀⢿⣿⠀⠀⠀⠀⠀⣾⠀⠘⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠓⣦⠀⠀⠀⠀⢠⣿⣿⣿⠀⠘⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⢸⣿⠀⠀⠐⠀⠀⣼⠛⠋⠀⠀⣀⠀⠀⠀⠤⠀⠠⠀⠀⣀⣿⡇⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣿⡀⠀⠀⠀⠀⠀⢶⣤⡀⠀⠻⣷⣄⠀⠀⢰⡄⠀⠀⠙⠋⠀⣶⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠐⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⣶⡆⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠠⠀⣀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⢿⣷⡄⢠⠀⠀⢰⣾⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠻⠄⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠉⣿⢇⣀⡈⠀⠀⠙⠁⠀⠹⣿⡿⠋⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣤⣾⣧⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣧⡄⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⠘⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣀⠙⢛⣛⣀⣄⡀⠀⠀⠀⣠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣄⠀⠀⠀⠀⠀⣴⣆⠐⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠺⠿⠿⢿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⠀⠀⠈⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣦⣴⣤⣤⣤⣶⣶⣶⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⢺⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠸⠆⠀⠏⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠘⠀⣠⠋⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠈⣁⡤⣔⠁⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠉⢃⠀⠀⠘⠋⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠈⡆⠀⠀⠘⣉⣱⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣣⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠬⢰⣋⣀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠈⢿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠿⡟⣭⠑⠀⠀⠀⠀⠀⣇⣀⠀⡸⠴⢩⡙⡿⠯⠤⠀⠀⠀⠀⠘⣿⣿⡇⠀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠉⡰⠀⠀⠀⡠⠄⠤⡀⠀⠀⠱⡘⠁⣇⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠈⠉⠀⢀⡠⠔⢀⠀⢀⠑⠤⣀⠀⠈⠉⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠠⡅⠀⠀⠀⠀⠈⠀⡀⠀⡅⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢣⠀⠀⠄⠀⠀⠌⠀⢠⠁⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⢀⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⡼⠀⠀⠸⣀⡐⠀⠀⠸⡀⠀⠀⠀⠄⠐⡀⠀⠀⠀⣠⣆⠀⠀⢸⣿⣟⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⢀⠞⠁⠀⠀⡰⠋⠳⡀⠀⠀⠙⢆⠀⠁⠀⠀⡇⠀⠀⠀⠸⠟⠀⣠⣮⡀⠘⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣀⠠⠁⠀⠀⣀⢞⠁⠀⠀⢙⢄⡀⠀⠀⠁⢀⣠⠜⠁⠀⠀⠘⠀⠀⢿⣿⣿⣿⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⢀⠄⠊⠁⠘⡀⠀⠀⡎⠀⠉⠢⠄⠀⠋⠀⠀⠀⠀⠀⢼⣦⣤⣾⣿⠻⣿⣧⣤⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠆⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⡇⡆⠀⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠀⠀⠀⡰⠁⠀⠀⠡⡀⠀⠀⢀⡖⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠇⠀⢿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠁⠀⠀⠀⠀⠈⠒⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣶⣶⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠤⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢩⣤⠊⠉⠟⠯⣅⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣲⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡶⣤⠉⠛⢖⢺⠿⣶⡌⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠙⢥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠁⣺⣆⡸⠀⢈⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠖⠛⠳⠏⠁⠀⠁⠉⡔⠀⣄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠁⠈⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠡⠠⠘⠂⢀⠀⡄⠀⡠⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠂⠔⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢚⡲⢦⣤⠁⠂⢠⡁⠀⠀⠿⡄⢠⠀⢤⠀⠀⠀⠀⠀⢠⣀⢀⠀⡃⡴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⠠⢉⡤⠋⣀⠔⠀⠂⠐⢀⠔⡹⡊⠠⠔⠀⠀⠀⠆⠀⠙⠛⠓⢿⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠠⠤⢄⠹⠄⣘⣳⠀⡄⢁⠈⡠⢁⠚⡠⠈⡁⠀⠀⠠⠀⠀⠀⠀⠘⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⢈⡀⣉⣈⡃⠊⠄⠹⠐⡡⠀⠂⡖⢠⠃⠚⡀⠁⡠⡆⣤⠌⣢⠞⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⢋⢯⠔⣊⣡⠐⢣⠄⠼⢡⠀⠨⠐⠀⠐⠋⣛⣖⣀⠀⣲⣯⣥⠴⡏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⢙⣛⣃⣩⣍⡠⠠⠄⢀⠀⠀⠂⠀⠀⠐⠉⢿⣿⣣⣿⢱⢿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡗⠐⢂⣿⣥⡈⠤⢶⢧⣈⠐⠁⠀⠀⠀⠀⢀⠀⠙⢂⠛⢉⡍⢀⢼⣀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⡓⠺⠭⠭⣢⠁⣀⠄⠐⠀⠀⡀⠀⠀⢀⠀⡅⠀⢚⠖⣩⢃⡴⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣴⡟⠃⣈⣠⢄⠀⠀⠀⠀⠀⠀⠌⠀⠰⠀⠡⠋⠡⣁⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣧⣴⣭⣴⣄⡀⣠⣛⣨⣌⣂⣥⠋⣠⣦⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⣿⢿⡭⠟⢉⣱⣲⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠛⠛⣧⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣆⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⣀⡤⡆⣰⢟⠩⠀⠖⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠈⠀⠁⠀⢴⣩⠴⠶⡀⠀⣸⣧⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠐⠣⠤⠖⢛⠛⡛⢠⠏⠀⠄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣻⣛⣿⣙⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢊⡉⢉⣛⣻⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠰⡅⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢾⣗⣬⣧⣤⣢⣝⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠂⠠⡐⠛⣎⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠄⠀⠀⠉⢿⣥⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⠱⠳⢹⡄⠜⢆⠀⢳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣢⠀⢀⢣⡡⠈⢆⢁⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠠⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⡈⢧⠈⢆⢳⠠⣸⠦⠷⠾⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠓⢆⢈⠁⢀⠀⠀⣀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣵⢄⠳⣿⣤⡂⣑⣒⣠⢖⠏⣡⢵⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣿⠤⡀⡛⣚⠉⣙⠟⢡⡻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡀⠀⢴⠀⣯⠐⠒⢚⣧⠬⢽⣚⢂⣰⣿⠀⠂⣤⣤⠠⣤⡄⠰⣧⣀⡿⡈⢄⣭⠹⢻⠉⠺⠦⢼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡟⠛⢲⣤⢞⡒⣚⡿⢳⣀⡗⠶⡧⠬⣙⣢⡚⠠⢾⡥⠘⡯⣤⣉⣼⣊⣷⢈⠖⠚⣋⠶⣤⠎⢰⠾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠈⢾⡏⣤⠺⠶⢮⠀⠴⠷⠶⢛⡖⣀⠿⣜⣁⣰⣉⣿⠄⠐⣾⢧⣎⣩⢴⠰⠾⡴⣄⣀⣱⣀⢳⠖⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⣁⡍⣷⠐⣇⣠⡶⣶⢒⡉⠛⡇⠚⠫⠀⡴⣾⠛⣲⣾⣇⡼⢯⠘⢿⣶⣤⡄⡈⢋⢁⣄⣭⡴⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡆⣴⣿⡀⠘⡁⠾⣩⠙⡙⢋⠿⣾⣧⣴⣟⣩⠴⣯⢦⡀⡻⠲⣵⣏⣠⠃⡔⢻⡧⡻⣧⢧⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣏⣡⣾⢻⣇⡹⣎⣱⡹⠾⣤⢮⣄⡉⢳⠞⢛⣁⡤⢶⡆⣄⢴⡅⠹⢣⣆⡜⢱⡠⣴⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣻⣎⣻⣤⣷⣼⣌⣿⣱⢿⣿⡿⢛⣻⣿⢋⢻⣤⣾⢈⡿⢐⣯⣀⡁⢛⣴⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣾⣿⡯⣽⣉⣭⠍⢛⠿⡿⣿⠺⢉⣆⣭⣩⣤⣩⣍⣨⣷⣶⣿⣏⣤⣿⣯⡬⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⣻⣺⣿⣥⡶⢖⣯⡤⢾⣿⠌⠿⣍⣛⠧⠴⠾⠷⣻⡿⢿⣿⡿⣯⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⣿⣷⣶⣿⣭⣒⣫⡽⣉⣿⠟⣿⣿⣿⣾⣛⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⡿⣿⣿⣿⣿⣿⣿⣻⣿⣽⣦⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡟⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣳⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡽⣳⣿⣋⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠙⠉⣻⣿⣽⣿⣓⣤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⢦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⢠⢽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠚⣥⡴⠊⠹⠿⢏⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠐⠀⢸⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣴⢦⡙⠚⢷⡔⣺⢿⣦⡑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠄⠙⢯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠉⠠⣿⡅⡏⠀⠙⣗⠐⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠃⠀⠀⠃⠀⠀⠄⠘⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣵⠲⠾⡿⠟⠀⠔⠈⠋⡆⠐⡀⠀⠀⠀⠀⠠⠘⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡖⣃⣁⠶⠀⡀⢤⠃⠀⣁⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠃⡀⢀⠰⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠶⣤⣀⡰⠀⠒⢪⠃⠈⠀⣷⡀⢀⠀⣀⠈⠂⠀⠀⠀⢀⡀⢀⠀⠰⢠⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡂⣝⠳⡹⠟⢀⡤⠜⠄⠠⢀⡠⢧⠜⢀⡨⠀⠀⠀⣄⠀⠚⠿⢶⣶⣾⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠄⣀⣉⠁⣎⠉⠴⣞⠀⡰⠊⠐⢀⠃⠴⢀⠀⠂⡄⠀⠄⡀⠄⠘⠠⠙⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠁⠀⠈⠣⠨⠚⢻⡇⠔⡁⢾⡠⢃⠘⠀⣡⢂⡬⢰⠀⠀⢁⣠⢡⢀⢦⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⢿⣒⣩⠿⢂⣰⠅⡀⣠⢇⠈⢴⠹⡈⠠⠴⠶⣤⠜⠉⠸⡿⢾⣁⣾⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⠀⠀⠉⣯⠴⠾⢿⠄⣋⠉⠁⠘⠀⠨⡄⠠⠀⠀⠞⢿⣿⣶⢰⡿⣟⡧⡾⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡈⣠⢫⡿⡓⠒⣛⣛⠇⠙⠠⠖⠀⠇⠀⠆⠀⠀⠠⡌⣿⡿⢻⠃⣋⣿⢃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣥⡄⡾⠿⠗⣩⠁⠍⡉⢂⠀⠀⠐⢀⠀⢀⠀⡆⠄⢱⣦⠶⢿⢀⣿⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣫⣭⣽⡏⠜⠋⠅⡀⠠⠀⠂⠀⠀⡰⠆⠛⡆⡜⣭⠾⡶⡛⣱⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣧⣴⡚⣚⠵⢀⡀⠀⣀⣤⠠⠥⡎⠔⢡⠈⠠⢎⣴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⡿⣷⣶⣾⡶⣾⡷⠖⣻⣣⣾⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡟⠛⢯⣭⣤⣾⢗⡻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣇⠀⠀⠀⢉⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⡀⢀⣼⡿⠗⡀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⡀⠢⠶⢻⠃⡾⠳⠙⡀⠋⢸⡧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⣀⠀⢀⡂⠻⠖⣛⣋⣤⠀⣼⠗⠂⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠉⠙⠛⠋⠩⠉⠉⡰⠃⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠀⠀⠀⠀⢀⣀⣠⣤⡤⢶⣶⣶⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢛⣿⠋⢁⣠⡴⠶⠛⠋⠉⢀⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢞⡯⠁⠀⢸⣧⠾⠋⠁⠀⠀⠀⠀⣠⣟⣡⣤⡤⠶⠶⠶⠶⠶⠶⢶⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⠋⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢈⣹⣿⣿⣿⣿⣿⣿⡷⠶⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⢰⡟⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⣿⢰⣿⣿⣿⣷⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠿⣿⢟⣽⣿⣅⣀
⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣿⣿⣿⣿⠿⣛⡫⠽⠖⠒⠋⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠋⠛⠉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣭⣛⢿⣫⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⡢⡀⡀⠀⠀⠀⠀⠀⠀⢀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠉⣠⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣀⡀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⡀⠉⠻⣿⠷⠄
⠀⠀⠀⠀⠀⠀⢸⣯⣬⣤⣶⡿⠁⠀⢀⣀⣤⡶⠟⢻⣿⣿⣿⣿⣿⣟⣓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⣸⣟⣛⠻⣿⡇⢠⣴⣿⡿⠉⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⡑⠄⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠹⣦
⠀⠂⠤⠠⣠⣶⡿⠞⠛⠳⠶⣝⢿⣿⣿⣠⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢰⡦⠠⠀⠄⠆⠐⢰⣿⣦⠀⠚⢷
⠀⠀⢠⡾⠟⠉⠀⠀⠠⠂⠀⠬⠿⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⢀⣾⣿⣿⣶⣶⣾⣧
⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠲⠶⠤⢤⣄⡉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣠⣴⣿⡿⠿⠟⠛⠛⠋⠉
⣰⡏⠀⠀⠀⠀⠀⣠⣴⣊⣉⠀⠀⠀⠀⠠⣄⠠⢾⡿⠃⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣴⡾⠛⣋⠅
⣿⣷⠀⠀⠀⣰⣯⣭⣭⣉⡉⠉⠉⠓⠒⠒⣒⣚⣩⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣫⡶⠋
⠸⣿⣆⠀⣼⠃⠀⠀⠀⠈⠉⢻⡖⠒⠶⠤⢴⣶⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠈⠻⢦⣽⣆⠀⠀⠀⠀⠀⣸⠇⠀⢢⡀⠸⣿⣿⣿⣷⣹⣿⣿⡟⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣿⣦⣤⣤⡇⠀⠉⠛⠋⢻⢻⣿⣿⢳⡿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣻⣇⠀⠀⠀⠀⢏⣾⡿⠃⣫⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡟⣿⣷⣤⣤⣶⣿⠟⣡⣾⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⣿⠿⠟⣛⣩⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠷⠶⠶⠚⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⢦⡀
⠀⠀⠀⠀⠀⣀⠀⠁⠀⠀⠈⢉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂
⠀⠀⠀⠀⡎⠀⠁⠐⠚⠛⠯⡉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢠⡇
⠀⠀⠀⠀⡇⡔⠀⠀⣰⡄⠀⢸⡀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡼⢻
⠀⠀⠀⠀⠘⠲⠄⠀⠙⠁⠀⡘⠀⠀⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠊⠁⠀⠀⠀⠀⢸⡀
⠀⠀⢀⠀⠀⠀⠴⠀⠀⢆⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠈⠉⠉⠀⠀⠀⠐⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⡀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⡐⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⡀⠀⠀⠀⣧
⠀⠀⠀⠰⣄⣀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⠆⠀⠀⢹
⠀⠀⠀⠀⠈⠀⢒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠋⠀⢠⡏
⠀⠀⠀⠀⠀⠀⢃⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠢⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠈⠋⠶⡆⠀⠀⢀⡘⠀⠀⠀⠀⠀⠘⠢⣀⠀⡤⢀⣀⣀⣀⣀⡠⠤⠒⠉⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⡦⢤⠤⠤⠤⠤⠒⡞⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣄⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠂⠁⠀⢀⣉⣁⣆⠀⠟⠀⠈⠒⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠩⠐⢊⠃⠀⠁⢐⠶⣂⠤⠤⠀⠐⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠘⠊⠀⠀⡥

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢠⣞⠐⠊⠀⠀⠀⠀⠀⠀⠑⠂⣳⡄⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣾⣁⡛⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢛⣈⢷⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣼⣃⣘⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣁⣈⣧⢠⡄
⠀⠀⠀⠀⠀⠀⠀⣠⢠⣟⢘⣛⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣛⣃⢿⡆⣄
⠀⠀⠀⠀⠀⡀⣰⡏⡿⢟⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⡻⠿⢹⣆
⠀⠀⠀⠀⢰⡇⣿⣾⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣷⣿⢸⡆
⠀⠀⠀⡄⣿⣇⣏⣵⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⣝⣼⣿⢠
⠀⠀⢸⣿⢿⣿⢟⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡻⣿⡿⣿⡇
⠀⢠⢸⣿⣼⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣧⣿⡇⡄
⠀⣿⡟⣿⡿⣫⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣝⢿⣿⢻⣿
⢀⢹⣿⣼⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣧⣿⡏
⢸⣯⢿⣿⡿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣮⢿⣿⡿⣽
⠘⣿⣎⣿⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⣿⣱⣿
⢷⡹⣿⣿⣿⣏⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣽⣿⣿⣿⢏
⠸⣿⣎⢻⡟⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⢻⡟⣳⣿
⠀⠹⣿⣦⣷⣿⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢿⣿⣼⣰⣿⠏
⠈⢷⣮⡿⣿⣿⠇⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠸⣿⣿⠿⣣⡾
⠀⠈⢿⣷⣌⢻⡄⣿⣿⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⣿⣿⢠⡟⣡⣾⡿⠁
⠀⠀⢀⡙⢿⣷⣿⣿⣿⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⣿⣿⣾⡿⠋⡀
⠀⠀⠈⠻⣶⣝⡻⠿⣿⠘⣿⣷⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣾⣿⠇⣽⠿⢟⣫⣶⡟⠁
⠀⠀⠀⠀⠙⢿⣿⣦⣜⢷⣽⣿⡇⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢰⣿⣯⡾⣣⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⣉⠻⠿⣷⣿⣿⣇⠘⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠃⣸⣿⣿⣾⡿⠟⢉
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣭⣉⠙⢷⣬⡻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢟⣥⡾⠋⣉⣥⣴⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣬⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣭⣶⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠙⠻⢷⣶⣤⣄⣀⣀⣠⣤⣶⡾⠟⠋⠉⠛⠛⠛⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣾⣿⣟⣛⣛⣻⣿⣷⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣤⣶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢿⠇⠀⡹⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⣔⣦⡑⣻⢗⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣿⣿⣿⠿⠿⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣷⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢟⠁⠀⠀⠀⢘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣼⡆⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡷⠀⠀⠀⠀⣲⣿⣿⣷⣶⡶⠦⣤⣤⣴⣶⣶⣾⣿⣿⣗⣉⣻⡇⢈⠟⣻⠗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡃⠀⢀⣶⣿⣿⡛⢲⣾⡭⢽⡖⠾⣿⣏⣽⠿⢿⣿⣦⣍⣹⡯⠉⢉⣿⣚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⢠⣾⣿⣿⣉⣛⣿⠟⠺⣏⣩⡿⢋⡤⠉⠀⠤⠌⡋⢻⣶⣌⣉⣿⣃⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡄⣿⡿⠛⠠⢭⣿⣉⣻⣾⡥⠟⣩⣯⣴⣾⡛⠛⡛⠛⣿⣿⣿⣧⣬⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣰⣿⣷⣶⣶⣾⣷⠾⣟⡪⣞⣽⣟⠿⢻⣂⠙⢳⣅⣄⡽⠀⠄⠘⠿⠛⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠈⠀⠀⠈⠉⠛⠿⠛⣿⢿⣿⣍⠓⠀⠉⠋⠉⣁⡀⠀⠉⠁⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢀⡄⠀⡀⣀⢀⣀⣠⣄⡀⠁⠀⠀⠀⢠⡤⣀⢰⣿⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣧⣕⣾⣽⣙⣋⣚⠟⢿⣿⡇⠀⠈⣷⠄⡁⠉⠲⣽⣿⣯⡇⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣍⣿⣿⣿⣿⣿⣷⣾⣻⣿⡄⠀⠩⣧⣿⠤⠀⠨⣿⣿⣧⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠟⠛⠿⣿⣻⣮⡛⢿⣄⡱⣹⣛⢳⣤⣤⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠟⠁⠀⠀⠁⠉⠈⠀⠘⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠞⡷⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣤⣤⣤⣴⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣄⣾⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠹⠟⠉⣠⣶⠿⠟⣻⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠉⠀⠀⠀⠉⠙⠛⠿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢀⣆⣀⣀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⡟⠋⠀⠀⠀⠀⠀⣰⡿⣿⣷⣾⢾⠘⣠⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀
⠀⠀⠀⠀⠀⢀⠄⠊⠁⢀⣤⣤⣤⠡⡀⠀⠀⠀⠀⠰⢯⠳⢌⣉⠡⠊⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠶⠄
⠀⠀⠀⢀⠔⠁⠀⠀⢀⣀⣀⣀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠁⠒⠀⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⡀
⠀⠀⠀⣇⠠⠐⠊⠉⠀⠀⢀⣀⣈⡉⠀⠒⠊⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠈⠳⣄
⠀⠀⠀⠉⠒⠒⠒⠈⠁⠀⡇⠀⢹⠉⠉⠙⢶⡶⠾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣤⣀⣈⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⠉⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⡀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢠⢣⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣰⠃⠀⡄⠀⠀⢠⡀⠀⣷⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⠀⣧⠀⢀⣾⣇⣠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠂⠤⣈⡢
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣁⣴⠂⠀⣿⣶⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⣛⠟⠋⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠘⠀⢒⠏⠀⠀⠀⠀⠈⠛⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⢹⡆
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡙⠻⠿
⠀⠀⠀⢀⠊⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⣳⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⢀⡴⠋⠁⢀⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠹
⠾⠷⠖⣩⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠡⠙⠳⣦
⠀⠀⣼⣇⣀⡠⣴⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠙⢗⠠⠇
⠀⠀⠉⠉⠁⡔⠁⢀⡤⢺⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠠⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡙⠒⠤⠇
⠀⠀⠀⠀⠾⠤⠚⠉⠀⡇⠀⢀⡴⡙⠀⠀⠀⣰⠁⠀⠀⢣⠀⠀⠀⠀⢇⠀⠀⠀⠀⠘⢷⣄⡀⠀⠈⢲⣄⣀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠴⠋⡰⠁⠀⢀⠜⡏⠀⢀⡆⠈⣆⠀⠀⠀⡌⣆⠀⢲⣤⣀⢈⣏⠙⠶⣤⣀⣳⡈⠉⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡤⠖⠁⠀⢧⡴⠋⢡⢀⡟⢦⡀⠀⣿⢾⣆⠈⣷⠈⠙⠋⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠻⢶⡿⠀⠈⠳⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⢿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣷⣶⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠋⠈⠉⠉⠉⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣶⣿⠟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⣰⣿⠟⠁⢠⣿⣿⣾⡿⢿⣷⣦⡀⠀⠀⠀⢀⣴⣾⡿⠿⣿⣦⡄⠀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⣼⣿⡟⠁⣀⣀⠈⢿⣿⡀⠀⠀⣾⡿⠁⢀⣀⠈⢻⣿⡆⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣿⣿⢀⣼⣿⣿⣇⠀⠛⠛⠀⣸⣿⠃⠀⠀⣿⣧⠀⠙⠛⠀⣸⣿⡇⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣾⡿⠁⠹⢿⣷⣦⣴⣾⡿⠋⠀⠀⠀⠙⢿⣷⣦⣴⣶⣿⠟⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⣿⣿⠋⠀⠀⠀⠀⠉⠉⠉⠁⠀⣀⣤⣤⣄⡀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠛⠛⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠇
⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠉⠉⠉⣻⣿⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠻⠟⠁⢀⣿⣟
⠀⠀⠀⠀⢀⣾⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⢸⣿⠿⣿⣶⣄
⠀⠀⠀⢠⣾⡟⢹⣿⡏⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣜⣿⡇⠀⠀⠀⣾⣿⠀⠀⠙⢿⣷
⠀⠀⢀⣿⡟⠀⠈⣿⣷⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣿⣿⣧⡀⠀⢀⣿⡏⠀⠀⠀⠈⣿
⠀⠀⣾⣿⠁⠀⠀⠘⣿⣧⡀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⠻⢿⣷⣾⣿⣃⠀⠀⠀⠀⣿
⠀⢠⣿⡏⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠙⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠿⢿⣿⣶⣾⡿
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠈⢻⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣄⠀⠙⠻⠏⠀⠀⠀⠀⠀⠀⣤⣤⠀⢠⣿⣿⣆
⠀⣼⣿⣿⣿⣶⣤⠀⠀⠀⢠⣿⡟⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⢀⣼⣿⠻⣿⡆
⣼⣿⠛⣿⣇⠉⠃⠀⠀⠀⣿⣿⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⢀⣴⣿⠟⠁⣠⣾⡿⠃⠀⣿⣿
⠀⠁⠀⠙⠉⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⢻⣿⡄⠀⠀⠘⢿⠟⠁⢀⣴⣿⠟⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠘⢿⣷⣀⣴⣾⡿⠋⠀⠀⠀⠀⠀⠀⢸⣿⡃⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣘⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣈⣛⣿⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣇⣀⣀
⣿⣿⡟⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠶⠇⠐⠇⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠲⢤⠀⡄⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐
⠀⢠⣾⣆⠀⠀⠀⠀⠀⠸⣿⡀⠀⡃⠀⠀⠀⠀⠀⠀⠸⢾⣿⡾⠐⢀⣰⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠂
⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠈⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠰⠟⠐⢲⣿⣿⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄
⠀⠀⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⠠⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣾⣿⠀⠣⡀⠀⠄⠀⠀⢀⠀⡀⠈⠀⠀⠀⠙⠛⠷⢦⣄⡀
⠀⠀⠀⠙⢿⣿⣷⣶⡶⠖⢠⡀⠀⠀⣀⠿⠖⠒⠒⠂⠀⠀⢰⣷⣿⠸⣧⠀⠈⠁⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⣴⡄⠀⠈⠁
⠀⠀⠀⠀⠘⣿⣧⠀⢰⡀⠘⢷⣤⠀⠀⠀⠀⣠⠀⠀⡀⠀⣾⣿⡇⠀⣿⡆⠀⠀⠀⠘⢷⣾⣿⠀⠀⠀⠀⢀⣼⣿⠇
⠀⠀⠀⠀⠀⢻⣿⣆⣮⣧⣤⠀⣿⣄⡄⠀⠀⡏⢀⡜⢀⣼⣿⣿⠁⠀⢸⣧⢧⣀⠀⠀⠀⠙⣿⠀⢀⣤⣶⣿⡿⠋⠀⣠⡆
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣌⢻⣧⣀⣼⣷⣾⣾⣿⣿⣿⠇⠀⠀⠈⢿⣎⢿⣿⡷⠀⢀⡸⠷⠛⠛⣩⠕⠂⢀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠈⠿⣷⣝⡛⠛⠋⠀⠀⣠⠘⠋⣀⣴⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣶⣦⣾⣟⣵⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢰⠆⡆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠻⠞⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠌⠀⠐⣤⠴⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠛⠀⢀⡈⠓⠀⡐⠋⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢨⡘⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⣄⡀⠀⢀⠀⢠⢀⠰⢄⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣼⣋⠦⣿⡅⠀⠦⢟⡿⢅⡀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣿⣿⠄⣈⣠⠄⠀⢸⣄⣈⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢺⡠⠏⠘⣷⣷⣾⣃⠀⣹⣧
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⣼⠱⡮⠶⢿⣿⠛⣿⣣⠻⡇
⠀⠀⠀⠀⢀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣎⢿⠉⠀⠁⠰⠞⣯⣆⣈⠠⠞⣣⡅
⠀⠀⠴⡉⠛⠁⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⡀⡆⠘⠃⢻⣤⡎⣭⠀⢹⠶⡆⠻⠳
⠀⠀⠀⠀⣰⠂⠉⠑⣀⡀⠀⢒⠀⠤⢙⡖⣣⠀⢤⠄⠠⠄⣀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⢀⠀⠀⠁⣤⠀⢰⡸⠄⠠⡇⠐⡆⠀⢀⠐⠁⡀
⠀⠀⠀⠰⠏⠀⠀⣈⣉⠋⢀⠙⠓⠺⢤⠀⠉⡙⠚⠂⠶⢀⣡⠄⠼⠯⠛⣾⣿⡔⣺⠷⠂⠀⠀⠈⢀⠰⠀⠀⠀⠀⡅⠀⠱⡈⢃⠀⡟⢩⠀⣀⣻⠇
⠀⠀⠀⠀⠀⠀⠀⣉⠁⠀⢉⠳⠶⠀⣆⠘⠧⠀⠤⠀⢀⡀⠆⣴⠀⠒⠶⡤⢠⡼⣣⡄⢲⠃⡄⠑⠜⠀⠑⠠⣃⠸⢃⠀⠁⠘⠃⠈⢁⡈⢀⣹⣏⢆
⠀⠀⠀⠀⠀⠀⢀⢙⡶⠂⠀⠐⠢⣤⠰⠆⠈⠁⣲⡄⢻⡝⢛⡡⢚⡞⠂⠀⢊⠀⣙⣁⢩⣀⣤⡴⢃⡐⢳⠀⠿⠀⠌⠀⠀⢀⡇⠀⠘⠉⠸⡋⢐⠚⡄
⠀⠀⠀⠀⠀⠀⠀⠺⠀⣀⡀⠊⣽⠉⢓⣴⡷⠈⣷⢀⡴⠰⡾⣁⣼⡟⢫⣀⣀⡉⣠⣍⣀⡠⢀⡤⠼⠀⠻⠛⠂⠆⡀⠆⠡⠀⠰⢦⢃⢈⠃⠙⢨⡓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢞⣻⣼⠗⢫⣐⡀⣹⣿⣜⣷⢺⡿⢏⣠⡽⢾⡍⠉⣼⡏⢉⠙⢀⠈⢠⠀⡀⠀⠠⠀⠀⢁⢀⣤⠞⠀⢠⡄⠋⣀⣌⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡨⠉⢠⠌⠐⢛⣷⣾⡿⣿⡿⠂⣠⠶⣙⡲⠿⠀⡀⢡⡄⢈⡁⠈⢠⠃⠀⡀⣡⡄⠀⡠⠊⠁⡇⠀⠘⠏⣦⡀⢟⠉⢢⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀⢩⣈⣤⡟⣶⡞⣟⡐⣯⡙⢁⣈⣀⣄⠀⢚⣱⠶⣿⡀⣤⠋⡀⢁⡼⢧⣤⠖⠑⢤⠃⠐⠉⢠⠈⡷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⢰⣦⣤⠵⠏⠑⢀⣭⠲⠿⣟⣿⣿⣽⣿⡿⠟⠻⡧⣌⡀⠈⣛⣾⣏⣶⡚⠗⠀⢸⠆⢻⡄⣀⣠⠰⣤⠛⠓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠅⠀⠚⣿⣯⣤⠀⠀⠀⡐⠉⠘⠢⠀⠉⠻⠚⠛⢶⠾⠒⡤⣞⠻⠫⠍⢋⠉⠐⠦⠀⠀⡅⢐⣸⠤⣏⠱⠾⢶⢇⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡁⠀⠘⠓⣢⠴⠀⠈⢣⡀⠂⣤⣄⣀⠀⢄⡀⣀⠄⣠⢀⠈⢠⠄⢀⡽⠂⡁⢀⣡⠀⣄⠘⠁⣼⣠⣴⢉⢹⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠠⠀⠀⣨⠏⠠⡬⠈⢭⡤⠙⠉⠐⠟⠉⠁⠘⠅⠀⠼⠉⠹⠉⠂⠿⠄⠐⠏⢰⣷⣺⡧⣾⣶⣽⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⢀⠠⣆⣀⣀⠀⣱⠀⠀⠀⠀⠐⠀⠄⠀⠈⢀⣂⣀⡐⠀⠂⣐⣠⠀⣿⣿⣾⡷⢯⠔⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠂⡈⠠⢶⣾⡿⠀⠀⠈⠁⠙⢉⢊⠋⠙⢉⣿⣿⣛⣷⣿⡿⠿⠟⠋⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠴⢿⣿⡊⠋⣰⣧⢶⣎⣸⣋⠘⣷⡿⠟⠟⡿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣘⢿⣍⡞⢃⠘⣻⣬⣻⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⠬⡿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠐⡈⠀⠈⠁⠀⠂⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠑⠀⠠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⠀⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡇⠀⠀⢸⣿⣿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠇⠀⠀⠸⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠉⠁⠀⠀⠀⠀⠈⠉⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣆⠀⠀⠀⠀⣠⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⡿⠿⠿⠛⠻⠿⠿⠿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠏⠀⠀⠀⣀⣤⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣤⣄⠀⠀⠀⠙⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠏⠀⠀⢀⣾⣿⡿⠟⠛⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠛⠛⢿⣿⣷⡄⠀⠀⠘⣿⣿⣿⣆
⠀⠀⠀⠀⠀⢀⣿⣿⣿⠏⠀⠀⠀⣼⣿⡟⠀⣴⣶⡄⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⣶⣦⠀⢹⣿⣿⠀⠀⠀⠸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⢹⣿⣷⡀⠉⠛⢁⣴⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡀⠙⠋⢀⣼⣿⡟⠀⠀⠀⠀⠹⣿⣿⣷
⠀⠀⠀⠀⢠⣿⣿⣿⠁⠀⠀⠀⠀⠀⠻⢿⣿⣿⣾⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢿⣿⣿⡆
⠀⠀⠀⠀⣼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷
⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⡿⠟⠛⠛⠻⢿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿
⠀⠀⠀⠀⠸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟
⠀⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⢸⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣤⡀⠀⠀⠈⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⠀⠀⠀⣠⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣄⡀⠘⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠏⢀⣠⣴⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣾⣿⣿⣿⡿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠃⠈⠙⠻⢿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠘⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿⣿⣦⡀⠀⠀⠀⣴⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣯⣤⣴⣶⣶⣿⣶⣶⣦⣄⡀⠀⠈⠻⣿⣿⣿⣄⣠⣾⣿⣿⡟⠁⠀⢀⣠⣴⣶⣶⣶⣶⣶⣤⣤⣄⣹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠛⠛⢿⣿⣷⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣾⣿⡿⠛⠛⠛⠛⠛⠿⠿⠿⢿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡏⠀⣀⣤⣤⣄⠉⠻⠟⠋⣠⣤⣄⡀⠀⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⣠⣾⣿⡿⢿⣿⣧⠀⢀⣾⣿⡿⣿⣿⣦⡀⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡿⠋⠀⠈⣿⣿⡆⢸⣿⣿⠀⠈⠻⣿⣿⣦⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋⠀⠀⠀⠀⢻⣿⣷⣾⣿⡇⠀⠀⠀⠈⠙⠿⠿⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣿⣿⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣶⣛⣹⣏⣹⣇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣐⡀⢠⡖⠄
⠀⠀⠀⠀⠀⢤⠤⠤⣀⠀⠀⠉⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⠉⠉⠛⢦⣑⢦⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣈⡙⠓⠦⣄⢈⠻⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⢀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀⡉⠳⣤⣠⣽⡟⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⢸⣆⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡟⠛⠃⠈⠉⠀⢀⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⡇⠀⠀⠀⣠⠖
⠀⠀⠻⣷⣤⣀⣼⣇⠀⠀⠀⠀⠀⢠⠿⢛⡲⢤⡀⠀⠀⠀⠀⠀⠀⡠⠌⠀⠀⠀⠀⣀⡤⠞⠀⡄⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠽⠷⢤⣶⡋⠁
⠀⠀⠀⣌⠉⠛⠛⠻⣦⣄⠀⣀⡴⠋⠀⠀⠉⢷⣝⢆⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⣴⠁⠀⠀⠀⠘⠢⣀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄
⠀⠀⠀⢹⣇⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⢀⡀⠀⣿⡾⠖⠒⠂⠃⠀⠀⠀⠀⠀⣾⢻⡆⠀⠀⠀⠀⠀⠀⠉⠓⢼⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣸⠛⢦⣄⡀
⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⢴⠖⠉⠀⠀⠀⠀⠀⠂⠀⠀⠀⣼⠇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣄⠀⠀⠀⠀⠀⠊⠁⠀⠀⠃⢠⡾⢹⡏
⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⠻⣷⣀⡀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢠⣾⡟⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⣶⣤⣄⣀⣀⣀⣠⠔⢲⣾⠏⠀⣿⠃
⠀⠀⠀⠀⠸⣷⡢⡀⠀⠀⠀⠀⠀⠈⡍⠁⠀⠀⠀⠀⠂⠀⠀⠀⣠⢜⣿⡿⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠉⠀⣀⣴⡿⠃⢀⢀⡿
⠀⠀⠀⠀⠀⠹⣿⣌⠻⣶⣶⣶⣄⠀⢿⣄⠀⠀⠀⣀⣀⣠⡴⣛⡵⢋⣼⠃⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⣇⠀⠀⢀⢠⣴⣾⡿⢋⣠⣴⢏⣿⠃
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣮⡙⠿⣿⣷⡘⢿⣦⣤⡾⠛⣻⠟⣻⠏⣠⣾⠃⠀⠀⠀⠀⠀⠘⢷⡀⢀⡀⠀⠀⠀⠀⠀⠉⠈⠉⠛⠚⡛⢉⣴⡿⢛⣥⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣌⡙⠻⣦⣍⣉⣠⡴⢋⡜⣡⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⢮⣿⡶⣦⣤⣤⣤⠀⠀⠀⣠⡾⠃⣸⣯⣼⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣬⣍⠋⣩⣴⠿⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⢀⣤⣴⣿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢶⡄⠀⣠⠾⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⠶⣄⣹⠀⠻⣴⠏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠈⢿⠀⠀⠛⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣧⣠⣤⣤⣤⣤⣴⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠳⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢦⡴⠋⠀⠀⠀⠀⣶⠒⢚⠛⠛⠛⢛⡛⠛⢛⡷⠀⠀⠀⠀⠹⢤⠴⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⢻⡄⠈⠁⠀⠀⠈⠁⢀⡾⠁⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⣸
⢻⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⢀⡟
⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠈⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠞⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣛⣲⣶⣶⣶⣶⣦⣤⣤⣤⣶⣶⣶⣶⣶⣚⣛⣛⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡋⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⡴⠶⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡇
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⢸⡇
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠉⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⣼⡏⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠞⠛⠉⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣼⡟⠀⢻⡟⢄
⠀⠀⠀⠀⠀⠀⡇⠀⢀⣀⣀⠤⠤⠖⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦⡀⠀⠀⢀⣼⡿⠁⠀⢸⡇⠈⢷⣦
⠀⠀⠀⠀⠀⠀⠙⠉⠉⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⡀⣠⣿⡿⠁⠀⠀⠈⣇⠀⠀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣼⣿⡟⠁⠀⠀⠀⠀⠛⠀⠀⠀⠹⣿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣏⠀⣼⣿⣿⣿⣿⠁⠀⠀⠀⢀⣾⣿⣷⡄⠀⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢿⣷⡄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣄⣿⣿⣿⣿⡏⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠈⢿⣿⣶⣤⣀⣀⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠙⣿⣿⣷⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⢰⣿⣆⠀⢸⣿⣿⡀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣌⠉⠉⠁⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠈⠙⠻⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡌⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣼⣿⡟⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⢡⣶⣷⣦
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣼⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢰⣿⠿⣿⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⡏⠀⣿⠀⠀⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣿⣿⣧⠀⢿⣆⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⣠⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣠⣄⣠⣾⡿⠋⠀⠸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⠋⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⠇⢹⣿⣿⣇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿
⢻⡿⠋⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣄⠀⣸⣿⣿⡏⠀⢹⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠻⣿⣦⣰⣿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⣿⡇⠀⠈⢿⣿⠋⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡄⠈⠙⢿⡇⠀⠀⠈⠟⠀⠀⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠛⠿⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⡿⠋⠙⠻⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣆
⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄
⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⢹⣿⡄
⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⣰⣿⠛⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⢻⣿⡆⣿⣷
⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⢻⣿⣷⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣿⣿⡟⢸⣿⡄
⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠁⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⣶⣄⡀⠈⠛⠿⠟⠋⠀⢸⣿⡇
⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠉⠀⠀⠈⠙⠻⣿⣦⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣀⣀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⢹⣿⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢿⣿⣿⣶⣶⣤⣤⣿⣷⠀⢀⡀⣾⣿
⠀⠀⠀⢘⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣼⡿⠉⠙⠛⠛⠀⢸⣷⣿⡇
⠀⠀⠀⣼⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠃⠀⠀⠀⠀⣼⣿⣿⣿⣿⡀
⠀⠀⠀⠙⠛⠋⠈⣿⣷⡀⠀⢀⣴⣆⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣶⣄⠀⠀⣰⣿⠏⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣴⣿⠟⣿⣧⡀⠀⠀⠀⣠⣿⣷⡀⠀⠀⠀⣠⣾⡿⢿⣷⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠈⠻⣿⣦⣤⣴⣿⠟⠻⣿⣦⣤⣾⡿⠋⠀⠀⠙⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣻⣋⣁⣀⣀⣈⣛⣟⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿